An Invitation to Quantum Cohomology

Kontsevich's Formula for Rational Plane Curves

Joachim Kock, Israel Vainsencher - Collection Progress in Mathematics

170 pages, parution le 15/12/2006

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Résumé

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 is 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 to 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 of 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.

Written for: Graduate students, researchers, mathematicians, geometers, physicists

Sommaire

Introduction
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

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	PAPIER
Éditeur(s)	Birkhäuser
Auteur(s)	Joachim Kock, Israel Vainsencher
Collection	Progress in Mathematics
Parution	15/12/2006
Nb. de pages	170
Format	16 x 24
Couverture	Broché
Poids	370g
Intérieur	Noir et Blanc
EAN13	9780817644567
ISBN13	978-0-8176-4456-7