An Invitation to Quantum Cohomology : Kontsevich's Formula for Rational Plane Curves
- Author
- Joachim Kock, Israel Vainsencher
- Publication Year
- 2007
- Publisher
- Springer
- Language
- English
- Document Type
- Book
- Faculty / Subject Heading
- Mathematics and Statistics
- Download Book Read book
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.
Keywords: Mathematics and Statistics / Grad / Algebraic geometry / Cohomology / Homology / Moduli space
