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Author Shafarevich, I. R. (Igorʹ Rostislavovich), 1923-2017,
Title Algebraicheskaya Geometriya. English
Basic algebraic geometry. 2 / Igor R. Shafarevich ; translated by Miles Reid.
Imprint Berlin : Springer, 2013.
Edition Third edition.

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Author Shafarevich, I. R. (Igorʹ Rostislavovich), 1923-2017,
Subject Geometry, Algebraic.
Alt Name Reid, Miles (Miles A.),
Shafarevich, I. R. (Igorʹ Rostislavovich), 1923-2017. Algebraicheskaya Geometriya.
Description 1 online resource
polychrome rdacc
Edition Third edition.
Contents Book 2: Schemes and Varieties. Schemes -- The Spec of a Ring -- Sheaves -- Schemes -- Products of Schemes -- Varieties -- Definitions and Examples -- Abstract and Quasiprojective Varieties -- Coherent Sheaves -- Classification of Geometric Objects and Universal Schemes -- Book 3: Complex Algebraic Varieties and Complex Manifolds. The Topology of Algebraic Varieties -- The Complex Topology -- Connectedness -- The Topology of Algebraic Curves -- Real Algebraic Curves -- Complex Manifolds -- Definitions and Examples -- Divisors and Meromorphic Functions -- Algebraic Varieties and Complex Manifolds -- Kohler Manifolds -- Uniformisation -- The Universal Cover -- Curves of a Parabolic Type -- Curves of Hyperbolic Type -- Uniformising Higher Dimensional Varieties -- Historical Sketch. Elliptic Integrals -- Elliptic Functions -- Abelian Integrals -- Riemann Surfaces -- The Inversion of Abelian Integrals -- The Geography of Algebraic Curves -- Higher Dimensional Geometry -- The Analytic Theory of Complex Manifolds -- Algebraic Varieties over Arbitrary Fields and Schemes.
Note Translated from the Russian.
Bibliography Note Includes bibliographical references and index.
Summary Shafarevich's Basic Algebraic Geometry has been a classic and universally used introduction to the subject since its first appearance over 40 years ago. As the translator writes in a prefatory note, ̀̀For all [advanced undergraduate and beginning graduate] students, and for the many specialists in other branches of math who need a liberal education in algebraic geometry, Shafarevichs book is a must.'' The second volume is in two parts: Book II is a gentle cultural introduction to scheme theory, with the first aim of putting abstract algebraic varieties on a firm foundation; a second aim is to introduce Hilbert schemes and moduli spaces, that serve as parameter spaces for other geometric constructions. Book III discusses complex manifolds and their relation with algebraic varieties, Khler geometry and Hodge theory. The final section raisesan important problem in uniformising higher dimensional varieties that has been widely studied as the ̀S̀hafarevich conjecture''. The style of Basic Algebraic Geometry 2 and its minimal prerequisites make it to a large extent independent of Basic Algebraic Geometry 1, and accessible to beginning graduate students in mathematics and in theoretical physics.
Note Print version record.
ISBN 9783642380105 (electronic bk.)
3642380107 (electronic bk.)
ISBN/ISSN 10.1007/978-3-642-38010-5
OCLC # 857714757
Additional Format Print version: Shafarevich, I.R. (Igor Rostislavovich), 1923- Algebraicheskaya Geometriya. English. Basic algebraic geometry. 2. Third edition 9783642380099 (OCoLC)850177123

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