量子コホモロジー入門 An Invitation to Quantum Cohomology : Kontsevich's Formula for Rational Plane Curves (Progress in Mathematics Vol.249) （2006. X, 166 p. w. 30 figs.）

量子コホモロジー入門<br>An Invitation to Quantum Cohomology : Kontsevich's Formula for Rational Plane Curves (Progress in Mathematics Vol.249) （2006. X, 166 p. w. 30 figs.）

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量子コホモロジー入門
An Invitation to Quantum Cohomology : Kontsevich's Formula for Rational Plane Curves (Progress in Mathematics Vol.249) （2006. X, 166 p. w. 30 figs.）

Kock, Joachim/ Vainsencher, Israel

ウェブストア価格 ¥18,751（本体¥17,047）
BIRKHÄUSER（2006発売）
外貨定価 US$ 89.99
ポイント 170pt

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製本 Hardcover:ハードカバー版／ページ数 166 p.
言語 ENG
商品コード 9780817644567

基本説明

This elementary introduction to stable maps and quantum cohomology presents the problem of counting rational plane curves mostly from the viewpoint of enumerative geometry; Emphasis is on examples, heuristic discussions, and simple applications to best convey the intuition behind the subject.

Full Description

This book is an elementary introduction to some ideas and techniques that have revolutionized enumerative geometry: stable maps and quantum cohomology. A striking demonstration of the potential of these techniques is provided by Kont- vich's famous formula, which solves a long-standing question: How many plane rational curves of degree d pass through 3d — 1 given points in general position? The formula expresses the number of curves for a given degree in terms of the numbers for lower degrees. A single initial datum is required for the recursion, namely, the case d = I, which simply amounts to the fact that through two points there is but one line. Assuming the existence of the Kontsevich spaces of stable maps and a few of their basic properties, we present a complete proof of the formula, and use the formula as a red thread in our Invitation to Quantum Cohomology. For more information about the mathematical content, see the Introduction. The canonical reference for this topic is the already classical Notes on Stable Maps and Quantum Cohomology by Fulton and Pandharipande [29], cited henceforth as FP-NOTES. We have traded greater generality for the sake of introducing some simplifications. We have also chosen not to include the technical details of the construction of the moduli space, favoring the exposition with many examples and heuristic discussions.

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.