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 npointed Curves  Stable Maps  Enumerative Geometry via Stable Maps  GromovWitten 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 GromovWitten 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 selfstudy, as a text for a minicourse 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 149155) 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.


Quantumcohomologie.


Teoria homológica.


Geometria algébrica.


Curvas planas.


geometry.

Form 
Electronic book

Author 
Vainsencher, Israel

LC no. 
2006924437 
ISBN 
9780817644956 

0817644954 

0817644563 

9780817644567 
