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Principles of algebraic geometry [[electronic resource] /] / Phillip Griffiths and Joseph Harris
| Principles of algebraic geometry [[electronic resource] /] / Phillip Griffiths and Joseph Harris |
| Autore | Griffiths Phillip |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley, 1994 |
| Descrizione fisica | 1 online resource (830 p.) |
| Disciplina | 516.35 |
| Altri autori (Persone) | HarrisJoseph |
| Collana | Wiley classics library |
| Soggetto topico | Geometry, Algebraic |
| ISBN |
1-283-24648-1
9786613246486 1-118-03252-7 1-118-03077-X |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Principles of Algebraic Geometry; CONTENTS; CHAPTER 0 FOUNDATIONAL MATERIAL; 1. Rudiments of Several Complex Variables; Cauchy's Formula and Applications; Several Variables; Weierstrass Theorems and Corollaries; Analytic Varieties; 2. Complex Manifolds; Complex Manifolds; Submanifolds and Subvarieties; De Rham and Dolbeault Cohomology; Calculus on Complex Manifolds; 3. Sheaves and Cohomology; Origins: The Mittag-Leffler Problem; Sheaves; Cohomology of Sheaves; The de Rham Theorem; The Dolbeault Theorem; 4. Topology of Manifolds; Intersection of Cycles; Poincaré Duality
Intersection of Analytic Cycles5. Vector Bundles, Connections, and Curvature; Complex and Holomorphic Vector Bundles; Metrics, Connections, and Curvature; 6. Harmonic Theory on Compact Complex Manifolds; The Hodge Theorem; Proof of the Hodge Theorem I: Local Theory; Proof of the Hodge Theorem II: Global Theory; Applications of the Hodge Theorem; 7. Kähler Manifolds; The Kähler Condition; The Hodge Identities and the Hodge Decomposition; The Lefschetz Decomposition; CHAPTER 1 COMPLEX ALGEBRAIC VARIETIES; 1. Divisors and Line Bundles; Divisors; Line Bundles; Chern Classes of Line Bundles 2. Some Vanishing Theorems and CorollariesThe Kodaira Vanishing Theorem; The Lefschetz Theorem on Hyperplane Sections; Theorem B; The Lefschetz Theorem on (1, 1)-classes; 3. Algebraic Varieties; Analytic and Algebraic Varieties; Degree of a Variety; Tangent Spaces to Algebraic Varieties; 4. The Kodaira Embedding Theorem; Line Bundles and Maps to Projective Space; Blowing Up; Proof of the Kodaira Theorem; 5. Grassmannians; Definitions; The Cell Decomposition; The Schubert Calculus; Universal Bundles; The Plücker Embedding; CHAPTER 2 RIEMANN SURFACES AND ALGEBRAIC CURVES; 1. Preliminaries Embedding Riemann SurfacesThe Riemann-Hurwitz Formula; The Genus Formula; Cases g = 0, 1; 2. Abel's Theorem; Abel's Theorem-First Version; The First Reciprocity Law and Corollaries; Abel's Theorem-Second Version; Jacobi Inversion; 3. Linear Systems on Curves; Reciprocity Law II; The Riemann-Roch Formula; Canonical Curves; Special Linear Systems I; Hyperelliptic Curves and Riemann's Count; Special Linear Systems II; 4. Plücker Formulas; Associated Curves; Ramification; The General Plücker Formulas I; The General Plücker Formulas II; Weierstrass Points; Plucker Formulas for Plane Curves 5. CorrespondencesDefinitions and Formulas; Geometry of Space Curves; Special Linear Systems III; 6. Complex Tori and Abelian Varieties; The Riemann Conditions; Line Bundles on Complex Tori; Theta-Functions; The Group Structure on an Abelian Variety; Intrinsic Formulations; 7. Curves and Their Jacobians; Preliminaries; Riemann's Theorem; Riemann's Singularity Theorem; Special Linear Systems IV; Torelli's Theorem; CHAPTER 3 FURTHER TECHNIQUES; 1. Distributions and Currents; Definitions; Residue Formulas; Smoothing and Regularity; Cohomology of Currents 2. Applications of Currents to Complex Analysis |
| Record Nr. | UNISA-996204093603316 |
Griffiths Phillip
|
||
| Hoboken, N.J., : Wiley, 1994 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Principles of algebraic geometry / / Phillip Griffiths and Joseph Harris
| Principles of algebraic geometry / / Phillip Griffiths and Joseph Harris |
| Autore | Griffiths Phillip |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley, 1994 |
| Descrizione fisica | 1 online resource (830 p.) |
| Disciplina | 516.35 |
| Altri autori (Persone) | HarrisJoseph |
| Collana | Wiley classics library |
| Soggetto topico | Geometry, Algebraic |
| ISBN |
1-283-24648-1
9786613246486 1-118-03252-7 1-118-03077-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Principles of Algebraic Geometry; CONTENTS; CHAPTER 0 FOUNDATIONAL MATERIAL; 1. Rudiments of Several Complex Variables; Cauchy's Formula and Applications; Several Variables; Weierstrass Theorems and Corollaries; Analytic Varieties; 2. Complex Manifolds; Complex Manifolds; Submanifolds and Subvarieties; De Rham and Dolbeault Cohomology; Calculus on Complex Manifolds; 3. Sheaves and Cohomology; Origins: The Mittag-Leffler Problem; Sheaves; Cohomology of Sheaves; The de Rham Theorem; The Dolbeault Theorem; 4. Topology of Manifolds; Intersection of Cycles; Poincaré Duality
Intersection of Analytic Cycles5. Vector Bundles, Connections, and Curvature; Complex and Holomorphic Vector Bundles; Metrics, Connections, and Curvature; 6. Harmonic Theory on Compact Complex Manifolds; The Hodge Theorem; Proof of the Hodge Theorem I: Local Theory; Proof of the Hodge Theorem II: Global Theory; Applications of the Hodge Theorem; 7. Kähler Manifolds; The Kähler Condition; The Hodge Identities and the Hodge Decomposition; The Lefschetz Decomposition; CHAPTER 1 COMPLEX ALGEBRAIC VARIETIES; 1. Divisors and Line Bundles; Divisors; Line Bundles; Chern Classes of Line Bundles 2. Some Vanishing Theorems and CorollariesThe Kodaira Vanishing Theorem; The Lefschetz Theorem on Hyperplane Sections; Theorem B; The Lefschetz Theorem on (1, 1)-classes; 3. Algebraic Varieties; Analytic and Algebraic Varieties; Degree of a Variety; Tangent Spaces to Algebraic Varieties; 4. The Kodaira Embedding Theorem; Line Bundles and Maps to Projective Space; Blowing Up; Proof of the Kodaira Theorem; 5. Grassmannians; Definitions; The Cell Decomposition; The Schubert Calculus; Universal Bundles; The Plücker Embedding; CHAPTER 2 RIEMANN SURFACES AND ALGEBRAIC CURVES; 1. Preliminaries Embedding Riemann SurfacesThe Riemann-Hurwitz Formula; The Genus Formula; Cases g = 0, 1; 2. Abel's Theorem; Abel's Theorem-First Version; The First Reciprocity Law and Corollaries; Abel's Theorem-Second Version; Jacobi Inversion; 3. Linear Systems on Curves; Reciprocity Law II; The Riemann-Roch Formula; Canonical Curves; Special Linear Systems I; Hyperelliptic Curves and Riemann's Count; Special Linear Systems II; 4. Plücker Formulas; Associated Curves; Ramification; The General Plücker Formulas I; The General Plücker Formulas II; Weierstrass Points; Plucker Formulas for Plane Curves 5. CorrespondencesDefinitions and Formulas; Geometry of Space Curves; Special Linear Systems III; 6. Complex Tori and Abelian Varieties; The Riemann Conditions; Line Bundles on Complex Tori; Theta-Functions; The Group Structure on an Abelian Variety; Intrinsic Formulations; 7. Curves and Their Jacobians; Preliminaries; Riemann's Theorem; Riemann's Singularity Theorem; Special Linear Systems IV; Torelli's Theorem; CHAPTER 3 FURTHER TECHNIQUES; 1. Distributions and Currents; Definitions; Residue Formulas; Smoothing and Regularity; Cohomology of Currents 2. Applications of Currents to Complex Analysis |
| Record Nr. | UNINA-9910139609303321 |
|
Griffiths Phillip
|
||
| Hoboken, N.J., : Wiley, 1994 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Rational homotopy theory and differential forms / / Phillip Griffiths, John Morgan
| Rational homotopy theory and differential forms / / Phillip Griffiths, John Morgan |
| Autore | Griffiths Phillip |
| Edizione | [2nd ed. 2013.] |
| Pubbl/distr/stampa | New York : , : Birkhauser, , 2013 |
| Descrizione fisica | 1 online resource (xi, 224 pages) : illustrations |
| Disciplina | 514.24 |
| Collana | Progress in Mathematics |
| Soggetto topico |
Homotopy theory
Differential forms |
| ISBN | 1-4614-8468-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1 Introduction -- 2 Basic Concepts -- 3 CW Homology Theorem -- 4 The Whitehead Theorem and the Hurewicz Theorem.- 5 Spectral Sequence of a Fibration -- 6 Obstruction Theory -- 7 Eilenberg-MacLane Spaces, Cohomology, and Principal Fibrations -- 8 Postnikov Towers and Rational Homotopy Theory -- 9 deRham's theorem for simplicial complexes -- 10 Differential Graded Algebras -- 11 Homotopy Theory of DGAs -- 12 DGAs and Rational Homotopy Theory -- 13 The Fundamental Group -- 14 Examples and Computations -- 15 Functorality -- 16 The Hirsch Lemma -- 17 Quillen's work on Rational Homotopy Theory -- 18 A1-structures and C1-structures -- 19 Exercises. |
| Record Nr. | UNINA-9910739407603321 |
|
Griffiths Phillip
|
||
| New York : , : Birkhauser, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||