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Author Kock, Joachim, 1967-

Title An invitation to quantum cohomology : Kontsevich's formula for rational plane curves / Joachim Kock, Israel Vainsencher
Published Boston : Birkhäuser, ©2007


Description 1 online resource (xii, 159 pages) : illustrations
Series Progress in mathematics ; vol. 249
Progress in mathematics (Boston, Mass.) ; v. 249.
Contents Prologue: Warming Up with Cross Ratios, and the Definition of Moduli Space -- Stable n-pointed Curves -- Stable Maps -- Enumerative Geometry via Stable Maps -- Gromov--Witten Invariants -- Quantum Cohomology
Summary "This book is an elementary introduction to stable maps and quantum cohomology, starting with an introduction to stable pointed curves, and culminating with a proof of the associativity of the quantum product. The viewpoint is mostly that of enumerative geometry, and the red thread of the exposition is the problem of counting rational plane curves. Kontsevich's formula in initially established in the framework of classical enumerative geometry, then as a statement about reconstruction for Gromov-Witten invariants, and finally, using generating functions, as a special case of the associativity of the quantum product." "Emphasis is given throughout the exposition of examples, heuristic discussions, and simple applications of the basic tools to best convey the intuition behind the subject. The book demystifies these new quantum techniques by showing how they fit into classical algebraic geometry." "Some familiarity with basic algebraic geometry and elementary intersection theory is assumed. Each chapter concludes with some historical comments and an outline to key topics and themes as a guide for further study, followed by a collection of exercises that complement the material covered and reinforce computational skills. As such, the book is ideal for self-study, as a text for a mini-course in quantum cohomology, or as a special topics text in a standard course in intersection theory. The book will prove equally useful to graduate students in the classroom setting as to researchers in geometry and physics who wish to learn about the subject."--Jacket
Notes Revised and expanded translation of the original Portuguese edition (A fórmula de Kontsevich para curvas racionais planas. Rio de Janeiro : Instituto de Matemática Pura e Aplicada, ©1999)
Bibliography Includes bibliographical references (pages 149-155) and index
Notes English
Print version record
In Springer eBooks
Subject Geometry, Enumerative.
Quantum theory.
Homology theory.
Curves, Plane.
Quantum Theory
Curves, Plane.
Geometry, Enumerative.
Homology theory.
Quantum theory.
Teoria homológica.
Geometria algébrica.
Curvas planas.
Form Electronic book
Author Vainsencher, Israel
LC no. 2006924437
ISBN 9780817644956
Other Titles Kontsevich's formula for rational plane curves