Mirror symmetry and algebraic geometry / David A. Cox, Sheldon Katz

Auteur principal : Cox, David A., 1948-, AuteurCo-auteur : Katz, Sheldon, 1956-, AuteurType de document : MonographieCollection : Mathematical surveys and monographs, 68Langue : anglais.Pays: Etats Unis.Éditeur : Providence : American Mathematical Society, 1999Description : 1 vol. (XXI-469 p.) ; 26 cmISBN: 0821810596.ISSN: 0885-4653.Bibliographie : Bibliogr. p. 437-451. Index.Sujet MSC : 14J32, Algebraic geometry - Surfaces and higher-dimensional varieties, Calabi-Yau manifolds
14N35, Projective and enumerative algebraic geometry, Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants
81T40, Quantum theory, Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81T45, Quantum theory, Topological field theories in quantum mechanics
32Q25, Several complex variables and analytic spaces - Complex manifolds, Calabi-Yau theory (complex-analytic aspects)
En-ligne : Zentralblatt | MathSciNet | AMS
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The book presents the very first comprehensive introduction to the algebro-geometric aspects of mirror symmetry. Taking into account that a reader who wants to learn about mirror symmetry has to face many tough obstacles, the authors have tried to arrange the material, in its full variety and complexity, in such a way that the entire text appears as being largely self-contained, systematizing, throughout well-motivated, reasonably detailed and complete, comprehensible, inspiring, and complementary to the current research literature. The book was primarily written to address the recent mathematical framework of mirror symmetry and, as far as possible, to show how this mathematical abstraction reflects the original spirit of the underlying physics. Accordingly, the authors had two primary target audiences in mind: Mathematicians wanting to learn about the recent developments in mirror symmetry, and physicists who are acquainted with mirror symmetry wanting to learn about the solid mathematical background of the subject. With all these ambitious, high-minded and methodologically very challenging goals in mind, the authors have succeeded to write a masterpiece of an encyclopaedic textbook that really leaves nothing to be desired. The contents of the book are arranged as follows: In their preface to the book, the authors explain the main goals they are striving for, the relation between mathematics and physics reflected by the text, and how to read the book in different ways. Then the text is divided into twelve chapters. (Zentralblatt)

Bibliogr. p. 437-451. Index

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