| 期刊全稱 | An Invitation to Quantum Cohomology | | 期刊簡稱 | Kontsevich‘s Formula | | 影響因子2023 | Joachim Kock,Israel Vainsencher | | 視頻video | http://file.papertrans.cn/156/155646/155646.mp4 | | 發(fā)行地址 | Elementary introduction to stable maps and quantum cohomology presents the problem of counting rational plane curves.Viewpoint is mostly that of enumerative geometry.Emphasis is on examples, heuristic | | 學科分類 | Progress in Mathematics | | 圖書封面 |  | | 影響因子 | 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 simplifi | | Pindex | Textbook 2007 |
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