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An Invitation to Quantum Cohomology
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An Invitation to Quantum Cohomology

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

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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Caractéristiques techniques

  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

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