An invitation to quantum cohomology : Kontsevich's formula for rational plane curves / Joachim Kock, Israel Vainsencher.
"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 expos...
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| Main Authors: | , |
|---|---|
| Format: | Ebook |
| Language: | English |
| Published: |
Boston :
Birkhäuser,
[2007]
|
| Series: | Progress in mathematics (Boston, Mass.) ;
v. 249. |
| Subjects: | |
| Online Access: | Springer eBooks |
MARC
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| 011 | |a EDS Title: An Invitation to Quantum Cohomology: Kontsevich's Formula for Rational Plane Curves | ||
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| 100 | 1 | |a Kock, Joachim, |d 1967- |e author. |9 435147 | |
| 245 | 1 | 3 | |a An invitation to quantum cohomology : |b Kontsevich's formula for rational plane curves / |c Joachim Kock, Israel Vainsencher. |
| 246 | 3 | 0 | |a Kontsevich's formula for rational plane curves |
| 264 | 1 | |a Boston : |b Birkhäuser, |c [2007] | |
| 264 | 4 | |c ©2007 | |
| 300 | |a 1 online resource (xii, 159 pages) : |b illustrations. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Progress in mathematics ; |v vol. 249 | |
| 500 | |a Revised and expanded translation of the original Portuguese edition (A fórmula de Kontsevich para curvas racionais planas. Rio de Janeiro : Instituto de Matemática Pura e Aplicada, c1999). | ||
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | 0 | |g 0 |t Prologue: Warming up with Cross Ratios, and the Definition of Moduli Space |g 5 -- |g 0.1 |t Cross ratios |g 5 -- |g 0.2 |t Definition of moduli space |g 11 -- |g 1 |t Stable n-pointed Curves |g 21 -- |g 1.1 |t n-pointed smooth rational curves |g 21 -- |g 1.2 |t Stable n-pointed rational curves |g 23 -- |g 1.3 |t Stabilization, forgetting marks, contraction |g 28 -- |g 1.4 |t Sketch of the construction of [Characters not reproducible subscript 0,n] |g 32 -- |g 1.5 |t The boundary |g 34 -- |g 1.6 |t Generalizations and references |g 39 -- |g 2 |t Stable Maps |g 47 -- |g 2.1 |t Maps P[superscript 1 Characters not reproducible] P[superscript r] |g 47 -- |g 2.2 |t 1-parameter families |g 54 -- |g 2.3 |t Kontsevich stable maps |g 58 -- |g 2.4 |t Idea of the construction of [Characters not reproducible subscript 0,n] (P[superscript r], d) |g 60 -- |g 2.5 |t Evaluation maps |g 63 -- |g 2.6 |t Forgetful maps |g 65 -- |g 2.7 |t The boundary |g 69 -- |g 2.8 |t Easy properties and examples |g 71 -- |g 2.9 |t Complete conics |g 74 -- |g 2.10 |t Generalizations and references |g 78 -- |g 3 |t Enumerative Geometry via Stable Maps |g 91 -- |g 3.1 |t Classical enumerative geometry |g 91 -- |g 3.2 |t Counting conics and rational cubics via stable maps |g 95 -- |g 3.3 |t Kontsevich's formula |g 99 -- |g 3.4 |t Transversality and enumerative significance |g 100 -- |g 3.5 |t Stable maps versus rational curves |g 102 -- |g 3.6 |t Generalizations and references |g 106 -- |g 4 |t Gromov-Witten Invariants |g 111 -- |g 4.1 |t Definition and enumerative interpretation |g 111 -- |g 4.2 |t Properties of Gromov-Witten invariants |g 115 -- |g 4.3 |t Recursion |g 117 -- |g 4.4 |t The reconstruction theorem |g 120 -- |g 4.5 |t Generalizations and references |g 123 -- |g 5 |t Quantum Cohomology |g 129 -- |g 5.1 |t Quick primer on generating functions |g 129 -- |g 5.2 |t The Gromov-Witten potential and the quantum product |g 132 -- |g 5.3 |t Associativity |g 136 -- |g 5.4 |t Kontsevich's formula via quantum cohomology |g 138 -- |g 5.5 |t Generalizations and references |g 141. |
| 520 | 1 | |a "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 in 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 of 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 to 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."--Jacket. | |
| 538 | |a Mode of access: World Wide Web. | ||
| 588 | |a Machine converted from AACR2 source record. | ||
| 650 | 0 | |a Curves, Plane. |9 349783 | |
| 650 | 0 | |a Geometry, Enumerative |9 373084 | |
| 650 | 0 | |a Homology theory. |9 333483 | |
| 650 | 0 | |a Quantum theory. |9 323053 | |
| 700 | 1 | |a Vainsencher, Israel, |e author. |9 859959 | |
| 830 | 0 | |a Progress in mathematics (Boston, Mass.) ; |v v. 249. |9 245956 | |
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