Principles of algebraic geometry / / Phillip Griffiths and Joseph Harris

• Autore: Griffiths Phillip
• Pubblicazione: Hoboken, N.J., : Wiley, 1994
• Descrizione fisica: 1 online resource (830 p.)
• Disciplina: 516.35
• Soggetto topico: Geometry, Algebraic
• Altri autori: HarrisJoseph
• Note generali: Originally published in 1978.
• Nota di bibliografia: Includes bibliographical references and index.
• 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
• Sommario/riassunto: A comprehensive, self-contained treatment presenting general results of the theory. Establishes a geometric intuition and a working facility with specific geometric practices. Emphasizes applications through the study of interesting examples and the development of computational tools. Coverage ranges from analytic to geometric. Treats basic techniques and results of complex manifold theory, focusing on results applicable to projective varieties, and includes discussion of the theory of Riemann surfaces and algebraic curves, algebraic surfaces and the quadric line complex as well as special top
• Titolo autorizzato: Principles of algebraic geometry
• ISBN: 1-283-24648-1; 9786613246486; 1-118-03252-7; 1-118-03077-X
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910139609303321
• Lo trovi qui: Univ. Federico II
• Serie: Wiley classics library.