Mirror Symmetry and Algebraic Geometry

David A. Cox, Sheldon Katz

470 pages, parution le 01/06/2001

Ajouter à une liste

Indisponible

Résumé

Mirror symmetry began when theoretical physicists made some astonishing predictions about rational curves on quintic hypersurfaces in four-dimensional projective space. Understanding the mathematics behind these predictions has been a substantial challenge. This book is the first completely comprehensive monograph on mirror symmetry, covering the original observations by the physicists through the most recent progress made to date. Subjects discussed include toric varieties, Hodge theory, Kähler geometry, moduli of stable maps, Calabi-Yau manifolds, quantum cohomology, Gromov-Witten invariants, and the mirror theorem. Features:

Numerous examples worked out in detail
An appendix on mathematical physics
An exposition of the algebraic theory of Gromov-Witten invariants and quantum cohomology
A proof of the mirror theorem for the quintic threefold

Contents

Preface
Notation
Ch. 1 Introduction 1
Ch. 2 The Quintic Threefold 15
Ch. 3 Toric Geometry 31
Ch. 4 Mirror Symmetry Constructions 53
Ch. 5 Hodge Theory and Yukawa Couplings 73
Ch. 6 Moduli Spaces 113
Ch. 7 Gromov-Witten Invariants 167
Ch. 8 Quantum Cohomology 217
Ch. 9 Localization 275
Ch. 10 Quantum Differential Equations 301
Ch. 11 The Mirror Theorem 331
Ch. 12 Conclusion 397
App. A Singular Varieties 407
App. B Physical Theories 411
Bibliography 437
Index

L'auteur - David A. Cox

DAVID A.COX is a professor of mathematics at Amherst College. He pursued his undergraduate studies at Rice University and earned his PhD from Princeton in 1975. The main focus of his research is algebraic geometry, though he also has interests in number theory and the history of mathematics. He is the author of Primes of the Form x² + ny², published by Wiley, as well as books on computational algebraic geometry and mirror symmetry.

Caractéristiques techniques

	PAPIER
Éditeur(s)	American Mathematical Society (AMS)
Auteur(s)	David A. Cox, Sheldon Katz
Parution	01/06/2001
Nb. de pages	470
Format	17,8 x 25,3
Couverture	Broché
Poids	852g
Intérieur	Noir et Blanc
EAN13	9780821821275
ISBN13	978-0-8218-2127-5