
An Invitation to Quantum Cohomology
Kontsevich's Formula for Rational Plane Curves
Joachim Kock, Israel Vainsencher - Collection Progress in Mathematics
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
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 |
Avantages Eyrolles.com
Nos clients ont également acheté
Consultez aussi
- Les meilleures ventes en Graphisme & Photo
- Les meilleures ventes en Informatique
- Les meilleures ventes en Construction
- Les meilleures ventes en Entreprise & Droit
- Les meilleures ventes en Sciences
- Les meilleures ventes en Littérature
- Les meilleures ventes en Arts & Loisirs
- Les meilleures ventes en Vie pratique
- Les meilleures ventes en Voyage et Tourisme
- Les meilleures ventes en BD et Jeunesse
- Sciences Mathématiques Mathématiques appliquées Mathématiques pour la physique
- Sciences Mathématiques Mathématiques appliquées Traitement du signal
- Sciences Mathématiques Logiciels de calcul
- Sciences Physique
- Sciences Physique Physique fondamentale Etats de la matière
- Sciences Physique Physique fondamentale Physique et mécanique quantique
- Sciences Physique Physique fondamentale Physique des particules
- Sciences Physique Physique fondamentale Physique nucléaire et atomique
- Sciences Etudes et concours Classes préparatoires et grandes écoles - Livres classes prépas scientifiques Physique