LEADER 05254nam 2200637 a 450 001 9910139609303321 005 20200520144314.0 010 $a1-283-24648-1 010 $a9786613246486 010 $a1-118-03252-7 010 $a1-118-03077-X 035 $a(CKB)2550000000045378 035 $a(EBL)708289 035 $a(OCoLC)751969638 035 $a(SSID)ssj0000613382 035 $a(PQKBManifestationID)11931513 035 $a(PQKBTitleCode)TC0000613382 035 $a(PQKBWorkID)10584415 035 $a(PQKB)10515616 035 $a(MiAaPQ)EBC708289 035 $a(PPN)254973140 035 $a(EXLCZ)992550000000045378 100 $a20111011d1994 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aPrinciples of algebraic geometry /$fPhillip Griffiths and Joseph Harris 210 $aHoboken, N.J. $cWiley$d1994 215 $a1 online resource (830 p.) 225 1 $aWiley classics library 300 $aOriginally published in 1978. 311 $a0-471-32792-1 311 $a0-471-05059-8 320 $aIncludes bibliographical references and index. 327 $aPrinciples 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; Poincare? Duality 327 $aIntersection 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. Ka?hler Manifolds; The Ka?hler 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 327 $a2. 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 Plu?cker Embedding; CHAPTER 2 RIEMANN SURFACES AND ALGEBRAIC CURVES; 1. Preliminaries 327 $aEmbedding 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. Plu?cker Formulas; Associated Curves; Ramification; The General Plu?cker Formulas I; The General Plu?cker Formulas II; Weierstrass Points; Plucker Formulas for Plane Curves 327 $a5. 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 327 $a2. Applications of Currents to Complex Analysis 330 $aA comprehensive, self-contained treatment presenting general results of the theory. Establishes a geometric intuition and a working facility with specific geometric practices. Emphasizes applications through the study of interesting examples and the development of computational tools. Coverage ranges from analytic to geometric. Treats basic techniques and results of complex manifold theory, focusing on results applicable to projective varieties, and includes discussion of the theory of Riemann surfaces and algebraic curves, algebraic surfaces and the quadric line complex as well as special top 410 0$aWiley classics library. 606 $aGeometry, Algebraic 615 0$aGeometry, Algebraic. 676 $a516.35 700 $aGriffiths$b Phillip$057421 701 $aHarris$b Joseph$0349615 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910139609303321 996 $aPrinciples of algebraic geometry$9835328 997 $aUNINA