**Student Mathematical Library**

Volume: 32;
2006;
206 pp;
Softcover

MSC: Primary 14;

Print ISBN: 978-0-8218-3687-3

Product Code: STML/32

List Price: $38.00

Individual Price: $30.40

**Electronic ISBN: 978-1-4704-2143-4
Product Code: STML/32.E**

List Price: $38.00

Individual Price: $30.40

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#### Supplemental Materials

# Enumerative Geometry and String Theory

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*Sheldon Katz*

Perhaps the most famous example of how ideas from modern
physics have revolutionized mathematics is the way string theory has led to an
overhaul of enumerative geometry, an area of mathematics that started in the
eighteen hundreds. Century-old problems of enumerating geometric configurations
have now been solved using new and deep mathematical techniques inspired by
physics!

The book begins with an insightful introduction to enumerative
geometry. From there, the goal becomes explaining the more
advanced elements of enumerative algebraic geometry. Along the way,
there are some crash courses on intermediate topics which are
essential tools for the student of modern mathematics, such as
cohomology and other topics in geometry.

The physics content assumes nothing beyond a first undergraduate
course. The focus is on explaining the action principle in physics,
the idea of string theory, and how these directly lead to questions in
geometry. Once these topics are in place, the connection
between physics and enumerative geometry is made with the introduction
of topological quantum field theory and quantum cohomology.

This book is published in cooperation with IAS/Park City Mathematics Institute

#### Table of Contents

# Table of Contents

## Enumerative Geometry and String Theory

- Cover Cover11 free
- Title i2 free
- Copyright ii3 free
- Contents v6 free
- IAS/Park City Mathematics Institute vii8 free
- Preface ix10 free
- Acknowledgements xii13 free
- Chapter 1. Warming up to Enumerative Geometry 116 free
- Chapter 2. Enumerative Geometry in the Projective Plane 1328
- Chapter 3. Stable Maps and Enumerative Geometry 2742
- Chapter 4. Crash Course in Topology and Manifolds 4358
- Chapter 5. Crash Course in C∞ Manifolds and Cohomology 5772
- Chapter 6. Cellular Decompositions and Line Bundles 7792
- Chapter 7. Enumerative Geometry of Lines 95110
- Chapter 8. Excess Intersection 111126
- Chapter 9. Rational Curves on the Quintic Threefold 125140
- Chapter 10. Mechanics 135150
- Chapter 11. Introduction to Supersymmetry 145160
- Chapter 12. Introduction to String Theory 157172
- Chapter 13. Topological Quantum Field Theory 173188
- Chapter 14. Quantum Cohomology and Enumerative Geometry 185200
- Bibliography 197212
- Index 201216
- Back Cover Backcover1224

#### Readership

Undergraduate and graduate students interested in algebraic geometry or in mathematical physics.

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