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Geometric theory of algebraic space curves / / S. S. Abhyankar and A. M. Sathaye
| Geometric theory of algebraic space curves / / S. S. Abhyankar and A. M. Sathaye |
| Autore | Abhyankar Shreeram Shankar |
| Edizione | [1st ed. 1974.] |
| Pubbl/distr/stampa | Berlin, Germany ; ; New York, New York : , : Springer-Verlag, , [1974] |
| Descrizione fisica | 1 online resource (XVI, 308 p.) |
| Disciplina | 510 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Curves, Algebraic
Mathematics Algebraic varieties |
| ISBN | 3-540-37280-6 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Local geometry of length -- Projective geometry or homogeneous domains -- Birational geometry or genus -- Affine geometry or filtered domains. |
| Record Nr. | UNISA-996466764303316 |
Abhyankar Shreeram Shankar
|
||
| Berlin, Germany ; ; New York, New York : , : Springer-Verlag, , [1974] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Lectures on algebra [[electronic resource] ] . Volume 1 / / S. S. Abhyankar
| Lectures on algebra [[electronic resource] ] . Volume 1 / / S. S. Abhyankar |
| Autore | Abhyankar Shreeram Shankar |
| Pubbl/distr/stampa | Hackensack, N.J., : World Scientific, c2006 |
| Descrizione fisica | 1 online resource (758 p.) |
| Disciplina | 512 |
| Soggetto topico |
Algebra, Abstract
Algebra Algebras, Linear |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-92476-8
9786611924768 981-277-344-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
CONTENTS; Lecture LI: Quadratic Equations; 1: Word Problems; 2: Sets and Maps; 3: Groups and Fields; 4: Rings and Ideals; 5: Modules and Vector Spaces; 6: Polynomials and Rational Functions; 7: Euclidean Domains and Principal Ideal Domains; 8: Root Fields and Splitting Fields; 9: Advice to the Reader; 10: Definitions and Remarks; 11: Examples and Exercises; 12: Notes; 13: Concluding Note; Lecture L2: Curves and Surfaces; 1: Multivariable Word Problems; 2: Power Series and Meromorphic Series; 3: Valuations; 4: Advice to the Reader; 5: Zorn's Lemma and Well Ordering; 6: Utilitarian Summary
7: Definitions and Exercises 8: Notes; 9: Concluding Note; Lecture L3: Tangents and Polars; 1: Simple Groups; 2: Quadrics; 3: Hypersurfaces; 4: Homogeneous Coordinates; 5: Singularities; 6: Hensel's Lemma and Newton's Theorem; 7: Integral Dependence; 8: Unique Factorization Domains; 9: Remarks; 10: Advice to the Reader; 11: Hensel and Weierstrass; 12: Definitions and Exercises; 13: Notes; 14: Concluding Note; Lecture L4: Varieties and Models; 1: Resultants and Discriminants; 2: Varieties; 3: Noetherian Rings; 4: Advice to the Reader; 5: Ideals and Modules; 6: Primary Decomposition 6.1: Primary Decomposition for Modules 7: Localization; 7.1: Localization at a Prime Ideal; 8: Affine Varieties; 8.1: Spectral Affine Space; 8.2: Modelic Spec and Modelic Affine Space; 8.3: Simple Points and Regular Local Rings; 9: Models; 9.1: Modelic Proj and Modelic Projective Space; 9.2: Modelic Blowup; 9.3: Blowup of Singularities; 10: Examples and Exercises; 11: Problems; 12: Remarks; 13: Definitions and Exercises; 14: Notes; 15: Concluding Note; Lecture L5: Projective Varieties; 1: Direct Sums of Modules; 2: Graded Rings and Homogeneous Ideals; 3: Ideal Theory in Graded Rings 4: Advice to the Reader 5: More about Ideals and Modules; (Ql) Nilpotents and Zerodivisors in Noetherian Rings; (Q2) Faithful Modules and Noetherian Conditions; (Q3) Jacobson Radical Zariski Ring and Nakayama Lemma; (Q4) Krull Intersection Theorem and Artin-Rees Lemma; (Q5) Nagata's Principle of Idealization; (Q6) Cohen's and Eakin's Noetherian Theorems; (Q7) Principal Ideal Theorems; (Q8) Relative Independence and Analytic Independence; (Q9) Going Up and Going Down Theorems; (Q10) Normalization Theorem and Regular Polynomials; (Qll) Nilradical Jacobson Spectrum and Jacobson Ring (Q12) Catenarian Rings and Dimension Formula(Q13) Associated Graded Rings and Leading Ideals; (Q14) Completely Normal Domains; (Q15) Regular Sequences and Cohen-Macaulay Rings; (Q16) Complete Intersections and Gorenstein Rings; (Q17) Projective Resolutions of Finite Modules; (Q18) Direct Sums of Algebras Reduced Rings and PIRs; (Q18.1) Orthogonal Idempotents and Ideals in a Direct Sum; (Q18.2) Localizations of Direct Sums; (Q18.3) Comaximal Ideals and Ideal Theoretic Direct Sums; (Q18.4) SPIRs = Special Principal Ideal Rings; (Q19) Invertible Ideals Conditions for Normality and DVRs (Q20) Dedekind Domains and Chinese Remainder Theorem |
| Record Nr. | UNINA-9910453620903321 |
|
Abhyankar Shreeram Shankar
|
||
| Hackensack, N.J., : World Scientific, c2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Lectures on algebra [[electronic resource] ] . Volume 1 / / S. S. Abhyankar
| Lectures on algebra [[electronic resource] ] . Volume 1 / / S. S. Abhyankar |
| Autore | Abhyankar Shreeram Shankar |
| Pubbl/distr/stampa | Hackensack, N.J., : World Scientific, c2006 |
| Descrizione fisica | 1 online resource (758 p.) |
| Disciplina | 512 |
| Soggetto topico |
Algebra, Abstract
Algebra Algebras, Linear |
| ISBN |
1-281-92476-8
9786611924768 981-277-344-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
CONTENTS; Lecture LI: Quadratic Equations; 1: Word Problems; 2: Sets and Maps; 3: Groups and Fields; 4: Rings and Ideals; 5: Modules and Vector Spaces; 6: Polynomials and Rational Functions; 7: Euclidean Domains and Principal Ideal Domains; 8: Root Fields and Splitting Fields; 9: Advice to the Reader; 10: Definitions and Remarks; 11: Examples and Exercises; 12: Notes; 13: Concluding Note; Lecture L2: Curves and Surfaces; 1: Multivariable Word Problems; 2: Power Series and Meromorphic Series; 3: Valuations; 4: Advice to the Reader; 5: Zorn's Lemma and Well Ordering; 6: Utilitarian Summary
7: Definitions and Exercises 8: Notes; 9: Concluding Note; Lecture L3: Tangents and Polars; 1: Simple Groups; 2: Quadrics; 3: Hypersurfaces; 4: Homogeneous Coordinates; 5: Singularities; 6: Hensel's Lemma and Newton's Theorem; 7: Integral Dependence; 8: Unique Factorization Domains; 9: Remarks; 10: Advice to the Reader; 11: Hensel and Weierstrass; 12: Definitions and Exercises; 13: Notes; 14: Concluding Note; Lecture L4: Varieties and Models; 1: Resultants and Discriminants; 2: Varieties; 3: Noetherian Rings; 4: Advice to the Reader; 5: Ideals and Modules; 6: Primary Decomposition 6.1: Primary Decomposition for Modules 7: Localization; 7.1: Localization at a Prime Ideal; 8: Affine Varieties; 8.1: Spectral Affine Space; 8.2: Modelic Spec and Modelic Affine Space; 8.3: Simple Points and Regular Local Rings; 9: Models; 9.1: Modelic Proj and Modelic Projective Space; 9.2: Modelic Blowup; 9.3: Blowup of Singularities; 10: Examples and Exercises; 11: Problems; 12: Remarks; 13: Definitions and Exercises; 14: Notes; 15: Concluding Note; Lecture L5: Projective Varieties; 1: Direct Sums of Modules; 2: Graded Rings and Homogeneous Ideals; 3: Ideal Theory in Graded Rings 4: Advice to the Reader 5: More about Ideals and Modules; (Ql) Nilpotents and Zerodivisors in Noetherian Rings; (Q2) Faithful Modules and Noetherian Conditions; (Q3) Jacobson Radical Zariski Ring and Nakayama Lemma; (Q4) Krull Intersection Theorem and Artin-Rees Lemma; (Q5) Nagata's Principle of Idealization; (Q6) Cohen's and Eakin's Noetherian Theorems; (Q7) Principal Ideal Theorems; (Q8) Relative Independence and Analytic Independence; (Q9) Going Up and Going Down Theorems; (Q10) Normalization Theorem and Regular Polynomials; (Qll) Nilradical Jacobson Spectrum and Jacobson Ring (Q12) Catenarian Rings and Dimension Formula(Q13) Associated Graded Rings and Leading Ideals; (Q14) Completely Normal Domains; (Q15) Regular Sequences and Cohen-Macaulay Rings; (Q16) Complete Intersections and Gorenstein Rings; (Q17) Projective Resolutions of Finite Modules; (Q18) Direct Sums of Algebras Reduced Rings and PIRs; (Q18.1) Orthogonal Idempotents and Ideals in a Direct Sum; (Q18.2) Localizations of Direct Sums; (Q18.3) Comaximal Ideals and Ideal Theoretic Direct Sums; (Q18.4) SPIRs = Special Principal Ideal Rings; (Q19) Invertible Ideals Conditions for Normality and DVRs (Q20) Dedekind Domains and Chinese Remainder Theorem |
| Record Nr. | UNINA-9910782318603321 |
|
Abhyankar Shreeram Shankar
|
||
| Hackensack, N.J., : World Scientific, c2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Lectures on algebra [[electronic resource] ] . Volume 1 / / S. S. Abhyankar
| Lectures on algebra [[electronic resource] ] . Volume 1 / / S. S. Abhyankar |
| Autore | Abhyankar Shreeram Shankar |
| Pubbl/distr/stampa | Hackensack, N.J., : World Scientific, c2006 |
| Descrizione fisica | 1 online resource (758 p.) |
| Disciplina | 512 |
| Soggetto topico |
Algebra, Abstract
Algebra Algebras, Linear |
| ISBN |
1-281-92476-8
9786611924768 981-277-344-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
CONTENTS; Lecture LI: Quadratic Equations; 1: Word Problems; 2: Sets and Maps; 3: Groups and Fields; 4: Rings and Ideals; 5: Modules and Vector Spaces; 6: Polynomials and Rational Functions; 7: Euclidean Domains and Principal Ideal Domains; 8: Root Fields and Splitting Fields; 9: Advice to the Reader; 10: Definitions and Remarks; 11: Examples and Exercises; 12: Notes; 13: Concluding Note; Lecture L2: Curves and Surfaces; 1: Multivariable Word Problems; 2: Power Series and Meromorphic Series; 3: Valuations; 4: Advice to the Reader; 5: Zorn's Lemma and Well Ordering; 6: Utilitarian Summary
7: Definitions and Exercises 8: Notes; 9: Concluding Note; Lecture L3: Tangents and Polars; 1: Simple Groups; 2: Quadrics; 3: Hypersurfaces; 4: Homogeneous Coordinates; 5: Singularities; 6: Hensel's Lemma and Newton's Theorem; 7: Integral Dependence; 8: Unique Factorization Domains; 9: Remarks; 10: Advice to the Reader; 11: Hensel and Weierstrass; 12: Definitions and Exercises; 13: Notes; 14: Concluding Note; Lecture L4: Varieties and Models; 1: Resultants and Discriminants; 2: Varieties; 3: Noetherian Rings; 4: Advice to the Reader; 5: Ideals and Modules; 6: Primary Decomposition 6.1: Primary Decomposition for Modules 7: Localization; 7.1: Localization at a Prime Ideal; 8: Affine Varieties; 8.1: Spectral Affine Space; 8.2: Modelic Spec and Modelic Affine Space; 8.3: Simple Points and Regular Local Rings; 9: Models; 9.1: Modelic Proj and Modelic Projective Space; 9.2: Modelic Blowup; 9.3: Blowup of Singularities; 10: Examples and Exercises; 11: Problems; 12: Remarks; 13: Definitions and Exercises; 14: Notes; 15: Concluding Note; Lecture L5: Projective Varieties; 1: Direct Sums of Modules; 2: Graded Rings and Homogeneous Ideals; 3: Ideal Theory in Graded Rings 4: Advice to the Reader 5: More about Ideals and Modules; (Ql) Nilpotents and Zerodivisors in Noetherian Rings; (Q2) Faithful Modules and Noetherian Conditions; (Q3) Jacobson Radical Zariski Ring and Nakayama Lemma; (Q4) Krull Intersection Theorem and Artin-Rees Lemma; (Q5) Nagata's Principle of Idealization; (Q6) Cohen's and Eakin's Noetherian Theorems; (Q7) Principal Ideal Theorems; (Q8) Relative Independence and Analytic Independence; (Q9) Going Up and Going Down Theorems; (Q10) Normalization Theorem and Regular Polynomials; (Qll) Nilradical Jacobson Spectrum and Jacobson Ring (Q12) Catenarian Rings and Dimension Formula(Q13) Associated Graded Rings and Leading Ideals; (Q14) Completely Normal Domains; (Q15) Regular Sequences and Cohen-Macaulay Rings; (Q16) Complete Intersections and Gorenstein Rings; (Q17) Projective Resolutions of Finite Modules; (Q18) Direct Sums of Algebras Reduced Rings and PIRs; (Q18.1) Orthogonal Idempotents and Ideals in a Direct Sum; (Q18.2) Localizations of Direct Sums; (Q18.3) Comaximal Ideals and Ideal Theoretic Direct Sums; (Q18.4) SPIRs = Special Principal Ideal Rings; (Q19) Invertible Ideals Conditions for Normality and DVRs (Q20) Dedekind Domains and Chinese Remainder Theorem |
| Record Nr. | UNINA-9910827165003321 |
|
Abhyankar Shreeram Shankar
|
||
| Hackensack, N.J., : World Scientific, c2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Local analytic geometry [[electronic resource] /] / Shreeram Shankar Abhyankar
| Local analytic geometry [[electronic resource] /] / Shreeram Shankar Abhyankar |
| Autore | Abhyankar Shreeram Shankar |
| Pubbl/distr/stampa | Singapore ; ; River Edge, NJ, : World Scientific, c2001 |
| Descrizione fisica | 1 online resource (504 p.) |
| Disciplina | 516.3 |
| Collana | Pure and applied mathematics; a series of monographs and textbooks |
| Soggetto topico |
Geometry, Analytic
Geometry, Algebraic |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-95185-4
9786611951856 981-281-034-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
PREFACE; INSTRUCTIONS TO THE READER; Contents; CHAPTER I Elementary Theory in Cn; 1. Notation and Terminology; 2. Convergent Power Series; 3. Laurent Series; 4. Cauchy Theory; 5. Convexity in Rn1; 6. Laurent Expansion in Cn; 7. Domains of Holomorphy; 8. A Theorem of Rado; 9. Comments on Totally Disconnected Fields; CHAPTER II Weierstrass Preparation Theorem; 10. Weierstrass Preparation Theorem. Identity Theorem. Finite Ideal Bases and Unique Factorization in Power Series Rings. Implicit Function Theorem; 11. Continuity of Roots and Open Map Theorem
12. Hensel's Lemma. Continuity of Algebroid Functions13. Complex Weierstrass Preparation Theorem; 14. Riemann Extension Theorem and Connectivity of Algebroid Hypersurfaces; 15. Oka Coherence; 16. Cartan Module Bases; CHAPTER III Review from Local Algebra; 17. Depth Height and Dimension. Completions. Direct Sums. Resultants and Discriminants; 18. Quotient Rings; 19. Integral Dependence and Finite Generation; 20. Henselian Rings; 21. Order and Rank in Local Rings. Regular Local Rings; 22. Another Proof that a Formal Power Series Rings is Noetherian; CHAPTER IV Parameters in Power Series Rings 23. Parameters for Ideals24. Perfect Fields; 25. Regularity of Quotient Rings; 26. Translates of Ideals; 27. Dimension of an Intersection; 28. Algebraic Lemmas on Algebroid Functions; CHAPTER V Analytic Sets; 29. The Language of Germs; 30. Decomposition of an Analytic Set Germ; 31. Ruckert-Weierstrass Parametrization of an Irreducible Analytic Set Germ; 32. Ruckert-Weierstrass Parametrization of an Irreducible Analytic Set Germ (Summary); 33. Local Properties of Analytic Sets; 34. Connectivity Properties of Complex Analytic Sets; 35. Parametrization of a Pure Dimensional Analytic Set 36. Normal Points of Complex Analytic Sets. Remarks on Algebraic Varieties37. Remmert-Stein-Thullen Theorem on Essential Singularities of Complex Analytic Sets. Theorem of Chow; 38. Topological Dimension; 39. Remarks on the Fundamental Group; CHAPTER VI Language of Sheaves; 40. Inductive Systems and Presheaves; 41. Sheaves; 42. Coherent Sheaves; CHAPTER VII Analytic Spaces; 43. Definitions; 44. Recapitulation of Properties of Analytic Spaces; 45. Invariance of Order and Rank; 46. Bimeromorphic Maps and Normalizations; BIBLIOGRAPHY; INDEX OF NOTATION; SUBJECT INDEX |
| Record Nr. | UNINA-9910454397003321 |
|
Abhyankar Shreeram Shankar
|
||
| Singapore ; ; River Edge, NJ, : World Scientific, c2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Local analytic geometry [[electronic resource] /] / Shreeram Shankar Abhyankar
| Local analytic geometry [[electronic resource] /] / Shreeram Shankar Abhyankar |
| Autore | Abhyankar Shreeram Shankar |
| Pubbl/distr/stampa | Singapore ; ; River Edge, NJ, : World Scientific, c2001 |
| Descrizione fisica | 1 online resource (504 p.) |
| Disciplina | 516.3 |
| Collana | Pure and applied mathematics; a series of monographs and textbooks |
| Soggetto topico |
Geometry, Analytic
Geometry, Algebraic |
| ISBN |
1-281-95185-4
9786611951856 981-281-034-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
PREFACE; INSTRUCTIONS TO THE READER; Contents; CHAPTER I Elementary Theory in Cn; 1. Notation and Terminology; 2. Convergent Power Series; 3. Laurent Series; 4. Cauchy Theory; 5. Convexity in Rn1; 6. Laurent Expansion in Cn; 7. Domains of Holomorphy; 8. A Theorem of Rado; 9. Comments on Totally Disconnected Fields; CHAPTER II Weierstrass Preparation Theorem; 10. Weierstrass Preparation Theorem. Identity Theorem. Finite Ideal Bases and Unique Factorization in Power Series Rings. Implicit Function Theorem; 11. Continuity of Roots and Open Map Theorem
12. Hensel's Lemma. Continuity of Algebroid Functions13. Complex Weierstrass Preparation Theorem; 14. Riemann Extension Theorem and Connectivity of Algebroid Hypersurfaces; 15. Oka Coherence; 16. Cartan Module Bases; CHAPTER III Review from Local Algebra; 17. Depth Height and Dimension. Completions. Direct Sums. Resultants and Discriminants; 18. Quotient Rings; 19. Integral Dependence and Finite Generation; 20. Henselian Rings; 21. Order and Rank in Local Rings. Regular Local Rings; 22. Another Proof that a Formal Power Series Rings is Noetherian; CHAPTER IV Parameters in Power Series Rings 23. Parameters for Ideals24. Perfect Fields; 25. Regularity of Quotient Rings; 26. Translates of Ideals; 27. Dimension of an Intersection; 28. Algebraic Lemmas on Algebroid Functions; CHAPTER V Analytic Sets; 29. The Language of Germs; 30. Decomposition of an Analytic Set Germ; 31. Ruckert-Weierstrass Parametrization of an Irreducible Analytic Set Germ; 32. Ruckert-Weierstrass Parametrization of an Irreducible Analytic Set Germ (Summary); 33. Local Properties of Analytic Sets; 34. Connectivity Properties of Complex Analytic Sets; 35. Parametrization of a Pure Dimensional Analytic Set 36. Normal Points of Complex Analytic Sets. Remarks on Algebraic Varieties37. Remmert-Stein-Thullen Theorem on Essential Singularities of Complex Analytic Sets. Theorem of Chow; 38. Topological Dimension; 39. Remarks on the Fundamental Group; CHAPTER VI Language of Sheaves; 40. Inductive Systems and Presheaves; 41. Sheaves; 42. Coherent Sheaves; CHAPTER VII Analytic Spaces; 43. Definitions; 44. Recapitulation of Properties of Analytic Spaces; 45. Invariance of Order and Rank; 46. Bimeromorphic Maps and Normalizations; BIBLIOGRAPHY; INDEX OF NOTATION; SUBJECT INDEX |
| Record Nr. | UNINA-9910782390103321 |
|
Abhyankar Shreeram Shankar
|
||
| Singapore ; ; River Edge, NJ, : World Scientific, c2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Local analytic geometry [[electronic resource] /] / Shreeram Shankar Abhyankar
| Local analytic geometry [[electronic resource] /] / Shreeram Shankar Abhyankar |
| Autore | Abhyankar Shreeram Shankar |
| Pubbl/distr/stampa | Singapore ; ; River Edge, NJ, : World Scientific, c2001 |
| Descrizione fisica | 1 online resource (504 p.) |
| Disciplina | 516.3 |
| Collana | Pure and applied mathematics; a series of monographs and textbooks |
| Soggetto topico |
Geometry, Analytic
Geometry, Algebraic |
| ISBN |
1-281-95185-4
9786611951856 981-281-034-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
PREFACE; INSTRUCTIONS TO THE READER; Contents; CHAPTER I Elementary Theory in Cn; 1. Notation and Terminology; 2. Convergent Power Series; 3. Laurent Series; 4. Cauchy Theory; 5. Convexity in Rn1; 6. Laurent Expansion in Cn; 7. Domains of Holomorphy; 8. A Theorem of Rado; 9. Comments on Totally Disconnected Fields; CHAPTER II Weierstrass Preparation Theorem; 10. Weierstrass Preparation Theorem. Identity Theorem. Finite Ideal Bases and Unique Factorization in Power Series Rings. Implicit Function Theorem; 11. Continuity of Roots and Open Map Theorem
12. Hensel's Lemma. Continuity of Algebroid Functions13. Complex Weierstrass Preparation Theorem; 14. Riemann Extension Theorem and Connectivity of Algebroid Hypersurfaces; 15. Oka Coherence; 16. Cartan Module Bases; CHAPTER III Review from Local Algebra; 17. Depth Height and Dimension. Completions. Direct Sums. Resultants and Discriminants; 18. Quotient Rings; 19. Integral Dependence and Finite Generation; 20. Henselian Rings; 21. Order and Rank in Local Rings. Regular Local Rings; 22. Another Proof that a Formal Power Series Rings is Noetherian; CHAPTER IV Parameters in Power Series Rings 23. Parameters for Ideals24. Perfect Fields; 25. Regularity of Quotient Rings; 26. Translates of Ideals; 27. Dimension of an Intersection; 28. Algebraic Lemmas on Algebroid Functions; CHAPTER V Analytic Sets; 29. The Language of Germs; 30. Decomposition of an Analytic Set Germ; 31. Ruckert-Weierstrass Parametrization of an Irreducible Analytic Set Germ; 32. Ruckert-Weierstrass Parametrization of an Irreducible Analytic Set Germ (Summary); 33. Local Properties of Analytic Sets; 34. Connectivity Properties of Complex Analytic Sets; 35. Parametrization of a Pure Dimensional Analytic Set 36. Normal Points of Complex Analytic Sets. Remarks on Algebraic Varieties37. Remmert-Stein-Thullen Theorem on Essential Singularities of Complex Analytic Sets. Theorem of Chow; 38. Topological Dimension; 39. Remarks on the Fundamental Group; CHAPTER VI Language of Sheaves; 40. Inductive Systems and Presheaves; 41. Sheaves; 42. Coherent Sheaves; CHAPTER VII Analytic Spaces; 43. Definitions; 44. Recapitulation of Properties of Analytic Spaces; 45. Invariance of Order and Rank; 46. Bimeromorphic Maps and Normalizations; BIBLIOGRAPHY; INDEX OF NOTATION; SUBJECT INDEX |
| Record Nr. | UNINA-9910816002403321 |
|
Abhyankar Shreeram Shankar
|
||
| Singapore ; ; River Edge, NJ, : World Scientific, c2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Ramification Theoretic Methods in Algebraic Geometry (AM-43), Volume 43 / / Shreeram Shankar Abhyankar
| Ramification Theoretic Methods in Algebraic Geometry (AM-43), Volume 43 / / Shreeram Shankar Abhyankar |
| Autore | Abhyankar Shreeram Shankar |
| Pubbl/distr/stampa | Princeton, NJ : , : Princeton University Press, , [2016] |
| Descrizione fisica | 1 online resource (117 pages) |
| Disciplina | 512.815 |
| Collana | Annals of Mathematics Studies |
| Soggetto topico |
Algebraic fields
Geometry, Algebraic |
| Soggetto non controllato |
Abelian group
Abstract algebra Additive group Affine variety Algebraic closure Algebraic curve Algebraic equation Algebraic function field Algebraic function Algebraic geometry Algebraic number theory Algebraic surface Algebraic variety Big O notation Birational geometry Branch point Cardinal number Cardinality Complex number Degrees of freedom (statistics) Dimension Equation Equivalence class Existential quantification Field extension Field of fractions Foundations of Algebraic Geometry Function field Galois group Generic point Ground field Homomorphism Ideal theory Integer Irrational number Irreducible component Linear algebra Local ring Mathematics Max Noether Maximal element Maximal ideal Natural number Nilpotent Noetherian ring Null set Order by Order type Parameter Primary ideal Prime ideal Prime number Projective variety Quantity Quotient ring Ramification group Rational function Rational number Real number Resolution of singularities Riemann surface Ring (mathematics) Special case Splitting field Subgroup Subset Theorem Theory of equations Transcendence degree Two-dimensional space Uniformization Valuation ring Variable (mathematics) Vector space Zero divisor Zorn's lemma |
| ISBN | 1-4008-8139-0 |
| Classificazione | SI 830 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- PREFACE -- CONTENTS -- INTRODUCTION -- CHAPTER I: GENERAL RAMIFICATION THEORY -- CHAPTER II: VALUATION THEORY -- CHAPTER III: NOETHERIAN LOCAL RINGS -- CHAPTER IV: TWO-DIMENSIONAL LOCAL DOMAINS -- CHAPTER V: VARIETIES AND TRANSFORMATIONS -- BIBLIOGRAPHY |
| Record Nr. | UNINA-9910154754403321 |
|
Abhyankar Shreeram Shankar
|
||
| Princeton, NJ : , : Princeton University Press, , [2016] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Weighted expansions for canonical desingularization / / Shreeram S. Abhyankar ; with foreword by U. Orbanz
| Weighted expansions for canonical desingularization / / Shreeram S. Abhyankar ; with foreword by U. Orbanz |
| Autore | Abhyankar Shreeram Shankar |
| Edizione | [1st ed. 1982.] |
| Pubbl/distr/stampa | Berlin ; ; Heidelberg ; ; New York : , : Springer-Verlag, , [1982] |
| Descrizione fisica | 1 online resource (VII, 238 p.) |
| Disciplina | 516.353 |
| Collana | Lecture notes in mathematics |
| Soggetto topico |
Geometry, Algebraic
Mappings (Mathematics) Singularities (Mathematics) |
| ISBN | 3-540-38992-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Notation -- Semigroups -- Strings -- Semigroup strings with restrictions -- Ordered semigroup strings with restrictions -- Strings on rings -- Indeterminate strings -- Indeterminate strings with restrictions -- Restricted degree and order for indeterminate strings -- Indexing strings -- Nets -- Semigroup nets with restrictions -- Ordered semigroup nets with restrictions -- Nets on rings -- Indeterminate nets -- Indeterminate nets with restrictions -- Restricted degree and order for indeterminate nets -- Prechips -- Isobars for prechips and Premonic polynomials -- Substitutions -- Substitutions with restrictions -- Coordinate nets and Monic polynomials -- Graded ring of a ring at an ideal -- Graded ring of a ring -- Graded rings at strings and nets and the notions of separatedness and regularity for strings and nets -- Inner products and further notions of separatedness and regularity for strings -- Inner products and further notions of separatedness and regularity for nets -- Weighted isobars and weighted initial forms -- Initial forms for regular strings -- Initial forms for regular strings and nets -- Protochips and parachips -- N-support of an indexing string for 2?N?6 -- Prescales -- Derived prescales -- Supports of prescales -- Protoscales -- Inner products for protoscales -- Scales and isobars -- Properties of derived prescales -- Isobars for derived scales -- Isobars and initial forms for scales -- Initial forms for scales and regular nets -- Isobars for protochips -- Initial forms for protochips and monic polynomials. |
| Record Nr. | UNISA-996466487103316 |
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Abhyankar Shreeram Shankar
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| Berlin ; ; Heidelberg ; ; New York : , : Springer-Verlag, , [1982] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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