An Invitation to Quantum Cohomology: Kontsevich's Formula for Rational Plane Curves (Progress in Mathematics)
| Author | : | |
| Rating | : | 4.44 (749 Votes) |
| Asin | : | 0817644563 |
| Format Type | : | paperback |
| Number of Pages | : | 162 Pages |
| Publish Date | : | 2017-08-25 |
| Language | : | English |
DESCRIPTION:
It makes the reader acquainted with the notions of stable curves and stable maps, and their moduli spaces. "The book seems to be ideally designed for a semester course or ambitious self-study." Mathematical Reviews"The book is intended to be a friendly introduction to quantum cohomology. This makes the book especially useful for graduate courses, and for graduate students who wish to learn about quantum cohomology." Zentralblatt Math"…The book is ideal for self-study, as a text for a mini-course in quantum
Elementary introduction to stable maps and quantum cohomology presents the problem of counting rational plane curvesViewpoint is mostly that of enumerative geometryEmphasis is on examples, heuristic discussions, and simple applications to best convey the intuition behind the subjectIdeal for self-study, for a mini-course in quantum cohomology, or as a special topics text in a standard course in intersection theory
A fine overview with helpful, pictorial examples The Kontsevich combinatorial formula of stable algebraic curves can be loosely described as being a generalization of what is done for Grassmann varieties in the context of vector bundles. A Grassmann variety Gr(k, n) is a collection L of k-dimensional linear subspaces of a complex n-dimensional vector space. The geometry of Gr(k, n) can be viewed as a kind of measure of how complicated things can get if L is permitted to vary in families. A family can be viewed as a collection of linear spaces parametrized by points of a base space B, and this leads naturally to the concept of a loc. John Matlock said New Theories in Enumerative Geometry. This book is an elementary introduction to some ideas and techniques that have revolutionized enumerative geometry: stable maps and quantum cohomology. It uses as a basis Kontsevich's formula and provides a complete proof of the formula.The book assumes some basic algebraic geometry and some elementary intersection theory. This would include algebraic curves, divisors and line bundles, blowup, Grassmannians.This book was originally published in Portuguese in 1999 as part of a mini-course. The further developments in the field have and the need for a more introductory book than Fulton. "Difficult !" according to M.Wick. Difficult reading without extensive mathematical background in quantum mechanics and modular theory.Equations require a PhD in advanced physics conceptually excellent