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Lectures on resolution of singularities [[electronic resource] /] / János Kollár
| Lectures on resolution of singularities [[electronic resource] /] / János Kollár |
| Autore | Kollár János |
| Edizione | [Course Book] |
| Pubbl/distr/stampa | Princeton, N.J., : Princeton University Press, 2007 |
| Descrizione fisica | 1 online resource (215 p.) |
| Disciplina | 516.3/5 |
| Collana | Annals of mathematics studies |
| Soggetto topico | Singularities (Mathematics) |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-282-15774-4
9786612157745 1-4008-2780-9 |
| Classificazione | SK 240 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- Contents -- Introduction -- Chapter 1. Resolution for Curves -- Chapter 2. Resolution for Surfaces -- Chapter 3. Strong Resolution in Characteristic Zero -- Bibliography -- Index |
| Record Nr. | UNINA-9910455256003321 |
Kollár János
|
||
| Princeton, N.J., : Princeton University Press, 2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Lectures on resolution of singularities [[electronic resource] /] / János Kollár
| Lectures on resolution of singularities [[electronic resource] /] / János Kollár |
| Autore | Kollár János |
| Edizione | [Course Book] |
| Pubbl/distr/stampa | Princeton, N.J., : Princeton University Press, 2007 |
| Descrizione fisica | 1 online resource (215 p.) |
| Disciplina | 516.3/5 |
| Collana | Annals of mathematics studies |
| Soggetto topico | Singularities (Mathematics) |
| Soggetto non controllato |
Adjunction formula
Algebraic closure Algebraic geometry Algebraic space Algebraic surface Algebraic variety Approximation Asymptotic analysis Automorphism Bernhard Riemann Big O notation Birational geometry C0 Canonical singularity Codimension Cohomology Commutative algebra Complex analysis Complex manifold Computability Continuous function Coordinate system Diagram (category theory) Differential geometry of surfaces Dimension Divisor Du Val singularity Dual graph Embedding Equation Equivalence relation Euclidean algorithm Factorization Functor General position Generic point Geometric genus Geometry Hyperplane Hypersurface Integral domain Intersection (set theory) Intersection number (graph theory) Intersection theory Irreducible component Isolated singularity Laurent series Line bundle Linear space (geometry) Linear subspace Mathematical induction Mathematics Maximal ideal Morphism Newton polygon Noetherian ring Noetherian Open problem Open set P-adic number Pairwise Parametric equation Partial derivative Plane curve Polynomial Power series Principal ideal Principalization (algebra) Projective space Projective variety Proper morphism Puiseux series Quasi-projective variety Rational function Regular local ring Resolution of singularities Riemann surface Ring theory Ruler Scientific notation Sheaf (mathematics) Singularity theory Smooth morphism Smoothness Special case Subring Summation Surjective function Tangent cone Tangent space Tangent Taylor series Theorem Topology Toric variety Transversal (geometry) Variable (mathematics) Weierstrass preparation theorem Weierstrass theorem Zero set |
| ISBN |
1-282-15774-4
9786612157745 1-4008-2780-9 |
| Classificazione | SK 240 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- Contents -- Introduction -- Chapter 1. Resolution for Curves -- Chapter 2. Resolution for Surfaces -- Chapter 3. Strong Resolution in Characteristic Zero -- Bibliography -- Index |
| Record Nr. | UNINA-9910778222903321 |
|
Kollár János
|
||
| Princeton, N.J., : Princeton University Press, 2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Lectures on resolution of singularities / / János Kollár
| Lectures on resolution of singularities / / János Kollár |
| Autore | Kollár János |
| Edizione | [Course Book] |
| Pubbl/distr/stampa | Princeton, N.J., : Princeton University Press, 2007 |
| Descrizione fisica | 1 online resource (215 p.) |
| Disciplina | 516.3/5 |
| Collana | Annals of mathematics studies |
| Soggetto topico | Singularities (Mathematics) |
| Soggetto non controllato |
Adjunction formula
Algebraic closure Algebraic geometry Algebraic space Algebraic surface Algebraic variety Approximation Asymptotic analysis Automorphism Bernhard Riemann Big O notation Birational geometry C0 Canonical singularity Codimension Cohomology Commutative algebra Complex analysis Complex manifold Computability Continuous function Coordinate system Diagram (category theory) Differential geometry of surfaces Dimension Divisor Du Val singularity Dual graph Embedding Equation Equivalence relation Euclidean algorithm Factorization Functor General position Generic point Geometric genus Geometry Hyperplane Hypersurface Integral domain Intersection (set theory) Intersection number (graph theory) Intersection theory Irreducible component Isolated singularity Laurent series Line bundle Linear space (geometry) Linear subspace Mathematical induction Mathematics Maximal ideal Morphism Newton polygon Noetherian ring Noetherian Open problem Open set P-adic number Pairwise Parametric equation Partial derivative Plane curve Polynomial Power series Principal ideal Principalization (algebra) Projective space Projective variety Proper morphism Puiseux series Quasi-projective variety Rational function Regular local ring Resolution of singularities Riemann surface Ring theory Ruler Scientific notation Sheaf (mathematics) Singularity theory Smooth morphism Smoothness Special case Subring Summation Surjective function Tangent cone Tangent space Tangent Taylor series Theorem Topology Toric variety Transversal (geometry) Variable (mathematics) Weierstrass preparation theorem Weierstrass theorem Zero set |
| ISBN |
1-282-15774-4
9786612157745 1-4008-2780-9 |
| Classificazione | SK 240 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- Contents -- Introduction -- Chapter 1. Resolution for Curves -- Chapter 2. Resolution for Surfaces -- Chapter 3. Strong Resolution in Characteristic Zero -- Bibliography -- Index |
| Record Nr. | UNINA-9910807941303321 |
|
Kollár János
|
||
| Princeton, N.J., : Princeton University Press, 2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Lectures on the Arithmetic Riemann-Roch Theorem. (AM-127), Volume 127 / / Gerd Faltings
| Lectures on the Arithmetic Riemann-Roch Theorem. (AM-127), Volume 127 / / Gerd Faltings |
| Autore | Faltings Gerd |
| Pubbl/distr/stampa | Princeton, NJ : , : Princeton University Press, , [2016] |
| Descrizione fisica | 1 online resource (113 pages) |
| Disciplina | 516.3/5 |
| Altri autori (Persone) | ZhangShouwu |
| Collana | Annals of Mathematics Studies |
| Soggetto topico |
Geometry, Algebraic
Riemann-Roch theorems |
| Soggetto non controllato |
Addition
Adjoint Alexander Grothendieck Algebraic geometry Analytic torsion Arakelov theory Asymptote Asymptotic expansion Asymptotic formula Big O notation Cartesian coordinate system Characteristic class Chern class Chow group Closed immersion Codimension Coherent sheaf Cohomology Combination Commutator Computation Covariant derivative Curvature Derivative Determinant Diagonal Differentiable manifold Differential form Dimension (vector space) Divisor Domain of a function Dual basis E6 (mathematics) Eigenvalues and eigenvectors Embedding Endomorphism Exact sequence Exponential function Generic point Heat kernel Injective function Intersection theory K-group Levi-Civita connection Line bundle Linear algebra Local coordinates Mathematical induction Morphism Natural number Neighbourhood (mathematics) Parameter Projective space Pullback (category theory) Pullback (differential geometry) Pullback Riemannian manifold Riemann–Roch theorem Self-adjoint operator Smoothness Sobolev space Stochastic calculus Summation Supertrace Theorem Transition function Upper half-plane Vector bundle Volume form |
| ISBN | 1-4008-8247-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- TABLE OF CONTENTS -- INTRODUCTION -- LIST OF SYMBOLS -- LECTURE 1. CLASSICAL RIEMANN-ROCH THEOREM -- LECTURE 2. CHERN CLASSES OF ARITHMETIC VECTOR BUNDLES -- LECTURE 3. LAPLACIANS AND HEAT KERNELS -- LECTURE 4. THE LOCAL INDEX THEOREM FOR DIRAC OPERATORS -- LECTURE 5. NUMBER OPERATORS AND DIRECT IMAGES -- LECTURE 6. ARITHMETIC RIEMANN-ROCH THEOREM -- LECTURE 7. THE THEOREM OF BISMUT-VASSEROT -- REFERENCES |
| Record Nr. | UNINA-9910154744103321 |
|
Faltings Gerd
|
||
| Princeton, NJ : , : Princeton University Press, , [2016] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Local and global methods in algebraic geometry : conference in honor of Lawrence Ein's 60th birthday, May 12-15, 2016, University of Illinois at Chicago, Chicago, Illinois / / Nero Budur [and three others], editors
| Local and global methods in algebraic geometry : conference in honor of Lawrence Ein's 60th birthday, May 12-15, 2016, University of Illinois at Chicago, Chicago, Illinois / / Nero Budur [and three others], editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2018] |
| Descrizione fisica | 1 online resource (370 pages) |
| Disciplina | 516.3/5 |
| Collana | Contemporary Mathematics |
| Soggetto topico |
Geometry, Algebraic
Festschriften Commutative algebra -- Theory of modules and ideals -- Linkage, complete intersections and determinantal ideals Algebraic geometry -- Local theory -- Singularities Algebraic geometry -- Families, fibrations -- Fibrations, degenerations Algebraic geometry -- Arithmetic problems. Diophantine geometry -- Rational points Algebraic geometry -- Surfaces and higher-dimensional varieties -- Special surfaces Algebraic geometry -- Surfaces and higher-dimensional varieties -- Vector bundles on surfaces and higher-dimensional varieties, and their moduli Several complex variables and analytic spaces -- Singularities -- Milnor fibration; relations with knot theory Differential geometry -- Local differential geometry -- Methods of Riemannian geometry |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-4850-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910479908603321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2018] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Local and global methods in algebraic geometry : conference in honor of Lawrence Ein's 60th birthday, May 12-15, 2016, University of Illinois at Chicago, Chicago, Illinois / / Nero Budur [and three others], editors
| Local and global methods in algebraic geometry : conference in honor of Lawrence Ein's 60th birthday, May 12-15, 2016, University of Illinois at Chicago, Chicago, Illinois / / Nero Budur [and three others], editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2018] |
| Descrizione fisica | 1 online resource (370 pages) |
| Disciplina | 516.3/5 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Geometry, Algebraic
Festschriften Commutative algebra -- Theory of modules and ideals -- Linkage, complete intersections and determinantal ideals Algebraic geometry -- Local theory -- Singularities Algebraic geometry -- Families, fibrations -- Fibrations, degenerations Algebraic geometry -- Arithmetic problems. Diophantine geometry -- Rational points Algebraic geometry -- Surfaces and higher-dimensional varieties -- Special surfaces Algebraic geometry -- Surfaces and higher-dimensional varieties -- Vector bundles on surfaces and higher-dimensional varieties, and their moduli Several complex variables and analytic spaces -- Singularities -- Milnor fibration; relations with knot theory Differential geometry -- Local differential geometry -- Methods of Riemannian geometry |
| ISBN | 1-4704-4850-5 |
| Classificazione | 13A3513C4014B0514D0614G0514J2514J6032B3232S5553B21 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910793047903321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2018] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Local and global methods in algebraic geometry : conference in honor of Lawrence Ein's 60th birthday, May 12-15, 2016, University of Illinois at Chicago, Chicago, Illinois / / Nero Budur [and three others], editors
| Local and global methods in algebraic geometry : conference in honor of Lawrence Ein's 60th birthday, May 12-15, 2016, University of Illinois at Chicago, Chicago, Illinois / / Nero Budur [and three others], editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2018] |
| Descrizione fisica | 1 online resource (370 pages) |
| Disciplina | 516.3/5 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Geometry, Algebraic
Festschriften Commutative algebra -- Theory of modules and ideals -- Linkage, complete intersections and determinantal ideals Algebraic geometry -- Local theory -- Singularities Algebraic geometry -- Families, fibrations -- Fibrations, degenerations Algebraic geometry -- Arithmetic problems. Diophantine geometry -- Rational points Algebraic geometry -- Surfaces and higher-dimensional varieties -- Special surfaces Algebraic geometry -- Surfaces and higher-dimensional varieties -- Vector bundles on surfaces and higher-dimensional varieties, and their moduli Several complex variables and analytic spaces -- Singularities -- Milnor fibration; relations with knot theory Differential geometry -- Local differential geometry -- Methods of Riemannian geometry |
| ISBN | 1-4704-4850-5 |
| Classificazione | 13A3513C4014B0514D0614G0514J2514J6032B3232S5553B21 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910818598403321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2018] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Local cohomology : an algebraic introduction with geometric applications / / M.P. Brodmann, University Zürich, R.Y. Sharp, University of Sheffield [[electronic resource]]
| Local cohomology : an algebraic introduction with geometric applications / / M.P. Brodmann, University Zürich, R.Y. Sharp, University of Sheffield [[electronic resource]] |
| Autore | Brodmann M. P (Markus P.), <1945-> |
| Edizione | [Second edition.] |
| Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2013 |
| Descrizione fisica | 1 online resource (xxii, 491 pages) : digital, PDF file(s) |
| Disciplina | 516.3/5 |
| Collana | Cambridge studies in advanced mathematics |
| Soggetto topico |
Algebra, Homological
Sheaf theory Commutative algebra |
| ISBN |
1-316-08882-0
1-107-47180-X 1-139-04405-2 1-139-78179-0 1-139-77576-6 1-139-79318-7 1-139-77880-3 1-139-77728-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Series Page; Title; Copyright; Dedication; Contents; Preface to the First Edition; Preface to the Second Edition; Notation and conventions; 1 The local cohomology functors; 1.1 Torsion functors; 1.2 Local cohomology modules; 1.3 Connected sequences of functors; 2 Torsion modules and ideal transforms; 2.1 Torsion modules; 2.2 Ideal transforms and generalized ideal transforms; 2.3 Geometrical significance; 3 The Mayer-Vietoris sequence; 3.1 Comparison of systems of ideals; 3.2 Construction of the sequence; 3.3 Arithmetic rank; 3.4 Direct limits; 4 Change of rings
4.1 Some acyclic modules4.2 The Independence Theorem; 4.3 The Flat Base Change Theorem; 5 Other approaches; 5.1 Use of Čech complexes; 5.2 Use of Koszul complexes; 5.3 Local cohomology in prime characteristic; 6 Fundamental vanishing theorems; 6.1 Grothendieck's Vanishing Theorem; 6.2 Connections with grade; 6.3 Exactness of ideal transforms; 6.4 An Affineness Criterion due to Serre; 6.5 Applications to local algebra in prime characteristic; 7 Artinian local cohomology modules; 7.1 Artinian modules; 7.2 Secondary representation; 7.3 The Non-vanishing Theorem again 8 The Lichtenbaum-Hartshorne Theorem8.1 Preparatory lemmas; 8.2 The main theorem; 9 The Annihilator and Finiteness Theorems; 9.1 Finiteness dimensions; 9.2 Adjusted depths; 9.3 The first inequality; 9.4 The second inequality; 9.5 The main theorems; 9.6 Extensions; 10 Matlis duality; 10.1 Indecomposable injective modules; 10.2 Matlis duality; 11 Local duality; 11.1 Minimal injective resolutions; 11.2 Local Duality Theorems; 12 Canonical modules; 12.1 Definition and basic properties; 12.2 The endomorphism ring; 12.3 S2-ifications; 13 Foundations in the graded case 13.1 Basic multi-graded commutative algebra13.2 *Injective modules; 13.3 The *restriction property; 13.4 The reconciliation; 13.5 Some examples and applications; 14 Graded versions of basic theorems; 14.1 Fundamental theorems; 14.2 *Indecomposable *injective modules; 14.3 A graded version of the Annihilator Theorem; 14.4 Graded local duality; 14.5 *Canonical modules; 15 Links with projective varieties; 15.1 Affine algebraic cones; 15.2 Projective varieties; 16 Castelnuovo regularity; 16.1 Finitely generated components; 16.2 The basics of Castelnuovo regularity; 16.3 Degrees of generators 17 Hilbert polynomials17.1 The characteristic function; 17.2 The significance of reg2; 17.3 Bounds on reg2 in terms of Hilbert coefficients; 17.4 Bounds on reg1 and reg0; 18 Applications to reductions of ideals; 18.1 Reductions and integral closures; 18.2 The analytic spread; 18.3 Links with Castelnuovo regularity; 19 Connectivity in algebraic varieties; 19.1 The connectedness dimension; 19.2 Complete local rings and connectivity; 19.3 Some local dimensions; 19.4 Connectivity of affine algebraic cones; 19.5 Connectivity of projective varieties; 19.6 Connectivity of intersections 19.7 The projective spectrum and connectedness |
| Record Nr. | UNINA-9910453139803321 |
|
Brodmann M. P (Markus P.), <1945->
|
||
| Cambridge : , : Cambridge University Press, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Local cohomology : an algebraic introduction with geometric applications / / M.P. Brodmann, University Zürich, R.Y. Sharp, University of Sheffield [[electronic resource]]
| Local cohomology : an algebraic introduction with geometric applications / / M.P. Brodmann, University Zürich, R.Y. Sharp, University of Sheffield [[electronic resource]] |
| Autore | Brodmann M. P (Markus P.), <1945-> |
| Edizione | [Second edition.] |
| Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2013 |
| Descrizione fisica | 1 online resource (xxii, 491 pages) : digital, PDF file(s) |
| Disciplina | 516.3/5 |
| Collana | Cambridge studies in advanced mathematics |
| Soggetto topico |
Algebra, Homological
Sheaf theory Commutative algebra |
| ISBN |
1-316-08882-0
1-107-47180-X 1-139-04405-2 1-139-78179-0 1-139-77576-6 1-139-79318-7 1-139-77880-3 1-139-77728-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Series Page; Title; Copyright; Dedication; Contents; Preface to the First Edition; Preface to the Second Edition; Notation and conventions; 1 The local cohomology functors; 1.1 Torsion functors; 1.2 Local cohomology modules; 1.3 Connected sequences of functors; 2 Torsion modules and ideal transforms; 2.1 Torsion modules; 2.2 Ideal transforms and generalized ideal transforms; 2.3 Geometrical significance; 3 The Mayer-Vietoris sequence; 3.1 Comparison of systems of ideals; 3.2 Construction of the sequence; 3.3 Arithmetic rank; 3.4 Direct limits; 4 Change of rings
4.1 Some acyclic modules4.2 The Independence Theorem; 4.3 The Flat Base Change Theorem; 5 Other approaches; 5.1 Use of Čech complexes; 5.2 Use of Koszul complexes; 5.3 Local cohomology in prime characteristic; 6 Fundamental vanishing theorems; 6.1 Grothendieck's Vanishing Theorem; 6.2 Connections with grade; 6.3 Exactness of ideal transforms; 6.4 An Affineness Criterion due to Serre; 6.5 Applications to local algebra in prime characteristic; 7 Artinian local cohomology modules; 7.1 Artinian modules; 7.2 Secondary representation; 7.3 The Non-vanishing Theorem again 8 The Lichtenbaum-Hartshorne Theorem8.1 Preparatory lemmas; 8.2 The main theorem; 9 The Annihilator and Finiteness Theorems; 9.1 Finiteness dimensions; 9.2 Adjusted depths; 9.3 The first inequality; 9.4 The second inequality; 9.5 The main theorems; 9.6 Extensions; 10 Matlis duality; 10.1 Indecomposable injective modules; 10.2 Matlis duality; 11 Local duality; 11.1 Minimal injective resolutions; 11.2 Local Duality Theorems; 12 Canonical modules; 12.1 Definition and basic properties; 12.2 The endomorphism ring; 12.3 S2-ifications; 13 Foundations in the graded case 13.1 Basic multi-graded commutative algebra13.2 *Injective modules; 13.3 The *restriction property; 13.4 The reconciliation; 13.5 Some examples and applications; 14 Graded versions of basic theorems; 14.1 Fundamental theorems; 14.2 *Indecomposable *injective modules; 14.3 A graded version of the Annihilator Theorem; 14.4 Graded local duality; 14.5 *Canonical modules; 15 Links with projective varieties; 15.1 Affine algebraic cones; 15.2 Projective varieties; 16 Castelnuovo regularity; 16.1 Finitely generated components; 16.2 The basics of Castelnuovo regularity; 16.3 Degrees of generators 17 Hilbert polynomials17.1 The characteristic function; 17.2 The significance of reg2; 17.3 Bounds on reg2 in terms of Hilbert coefficients; 17.4 Bounds on reg1 and reg0; 18 Applications to reductions of ideals; 18.1 Reductions and integral closures; 18.2 The analytic spread; 18.3 Links with Castelnuovo regularity; 19 Connectivity in algebraic varieties; 19.1 The connectedness dimension; 19.2 Complete local rings and connectivity; 19.3 Some local dimensions; 19.4 Connectivity of affine algebraic cones; 19.5 Connectivity of projective varieties; 19.6 Connectivity of intersections 19.7 The projective spectrum and connectedness |
| Record Nr. | UNINA-9910790698703321 |
|
Brodmann M. P (Markus P.), <1945->
|
||
| Cambridge : , : Cambridge University Press, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Local cohomology : an algebraic introduction with geometric applications / / M.P. Brodmann, University Zürich, R.Y. Sharp, University of Sheffield [[electronic resource]]
| Local cohomology : an algebraic introduction with geometric applications / / M.P. Brodmann, University Zürich, R.Y. Sharp, University of Sheffield [[electronic resource]] |
| Autore | Brodmann M. P (Markus P.), <1945-> |
| Edizione | [Second edition.] |
| Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2013 |
| Descrizione fisica | 1 online resource (xxii, 491 pages) : digital, PDF file(s) |
| Disciplina | 516.3/5 |
| Collana | Cambridge studies in advanced mathematics |
| Soggetto topico |
Algebra, Homological
Sheaf theory Commutative algebra |
| ISBN |
1-316-08882-0
1-107-47180-X 1-139-04405-2 1-139-78179-0 1-139-77576-6 1-139-79318-7 1-139-77880-3 1-139-77728-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Series Page; Title; Copyright; Dedication; Contents; Preface to the First Edition; Preface to the Second Edition; Notation and conventions; 1 The local cohomology functors; 1.1 Torsion functors; 1.2 Local cohomology modules; 1.3 Connected sequences of functors; 2 Torsion modules and ideal transforms; 2.1 Torsion modules; 2.2 Ideal transforms and generalized ideal transforms; 2.3 Geometrical significance; 3 The Mayer-Vietoris sequence; 3.1 Comparison of systems of ideals; 3.2 Construction of the sequence; 3.3 Arithmetic rank; 3.4 Direct limits; 4 Change of rings
4.1 Some acyclic modules4.2 The Independence Theorem; 4.3 The Flat Base Change Theorem; 5 Other approaches; 5.1 Use of Čech complexes; 5.2 Use of Koszul complexes; 5.3 Local cohomology in prime characteristic; 6 Fundamental vanishing theorems; 6.1 Grothendieck's Vanishing Theorem; 6.2 Connections with grade; 6.3 Exactness of ideal transforms; 6.4 An Affineness Criterion due to Serre; 6.5 Applications to local algebra in prime characteristic; 7 Artinian local cohomology modules; 7.1 Artinian modules; 7.2 Secondary representation; 7.3 The Non-vanishing Theorem again 8 The Lichtenbaum-Hartshorne Theorem8.1 Preparatory lemmas; 8.2 The main theorem; 9 The Annihilator and Finiteness Theorems; 9.1 Finiteness dimensions; 9.2 Adjusted depths; 9.3 The first inequality; 9.4 The second inequality; 9.5 The main theorems; 9.6 Extensions; 10 Matlis duality; 10.1 Indecomposable injective modules; 10.2 Matlis duality; 11 Local duality; 11.1 Minimal injective resolutions; 11.2 Local Duality Theorems; 12 Canonical modules; 12.1 Definition and basic properties; 12.2 The endomorphism ring; 12.3 S2-ifications; 13 Foundations in the graded case 13.1 Basic multi-graded commutative algebra13.2 *Injective modules; 13.3 The *restriction property; 13.4 The reconciliation; 13.5 Some examples and applications; 14 Graded versions of basic theorems; 14.1 Fundamental theorems; 14.2 *Indecomposable *injective modules; 14.3 A graded version of the Annihilator Theorem; 14.4 Graded local duality; 14.5 *Canonical modules; 15 Links with projective varieties; 15.1 Affine algebraic cones; 15.2 Projective varieties; 16 Castelnuovo regularity; 16.1 Finitely generated components; 16.2 The basics of Castelnuovo regularity; 16.3 Degrees of generators 17 Hilbert polynomials17.1 The characteristic function; 17.2 The significance of reg2; 17.3 Bounds on reg2 in terms of Hilbert coefficients; 17.4 Bounds on reg1 and reg0; 18 Applications to reductions of ideals; 18.1 Reductions and integral closures; 18.2 The analytic spread; 18.3 Links with Castelnuovo regularity; 19 Connectivity in algebraic varieties; 19.1 The connectedness dimension; 19.2 Complete local rings and connectivity; 19.3 Some local dimensions; 19.4 Connectivity of affine algebraic cones; 19.5 Connectivity of projective varieties; 19.6 Connectivity of intersections 19.7 The projective spectrum and connectedness |
| Record Nr. | UNINA-9910822393903321 |
|
Brodmann M. P (Markus P.), <1945->
|
||
| Cambridge : , : Cambridge University Press, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
