TY - BOOK
ED - SpringerLink (Online service)
TI - An Invitation to Quantum Cohomology: Kontsevich’s Formula for Rational Plane Curves
T2 - Progress in Mathematics
SN - 9780817644956
AV - QA564-609
U1 - 516.35 23
PY - 2007///
CY - Boston, MA
PB - Birkhäuser Boston
KW - Mathematics
KW - Algebraic geometry
KW - K-theory
KW - Applied mathematics
KW - Engineering mathematics
KW - Geometry
KW - Algebraic topology
KW - Physics
KW - Algebraic Geometry
KW - K-Theory
KW - Mathematical Methods in Physics
KW - Algebraic Topology
KW - Applications of Mathematics
N1 - 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
N2 - 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
UR - http://dx.doi.org/10.1007/978-0-8176-4495-6
ER -