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Tropical Geometry and Mirror Symmetry

Mark Gross University of California, San Diego, San Diego, CA
A co-publication of the AMS and CBMS
Available Formats:
Softcover ISBN: 978-0-8218-5232-3
Product Code: CBMS/114
List Price: $57.00 Individual Price:$45.60
Electronic ISBN: 978-1-4704-1572-3
Product Code: CBMS/114.E
List Price: $57.00 MAA Member Price:$51.30
AMS Member Price: $45.60 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version. List Price:$85.50
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Tropical Geometry and Mirror Symmetry
Mark Gross University of California, San Diego, San Diego, CA
A co-publication of the AMS and CBMS
Available Formats:
 Softcover ISBN: 978-0-8218-5232-3 Product Code: CBMS/114
 List Price: $57.00 Individual Price:$45.60
 Electronic ISBN: 978-1-4704-1572-3 Product Code: CBMS/114.E
 List Price: $57.00 MAA Member Price:$51.30 AMS Member Price: $45.60 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$85.50
• Book Details

CBMS Regional Conference Series in Mathematics
Volume: 1142011; 317 pp
MSC: Primary 14; 52;

Tropical geometry provides an explanation for the remarkable power of mirror symmetry to connect complex and symplectic geometry. The main theme of this book is the interplay between tropical geometry and mirror symmetry, culminating in a description of the recent work of Gross and Siebert using log geometry to understand how the tropical world relates the A- and B-models in mirror symmetry.

The text starts with a detailed introduction to the notions of tropical curves and manifolds, and then gives a thorough description of both sides of mirror symmetry for projective space, bringing together material which so far can only be found scattered throughout the literature. Next follows an introduction to the log geometry of Fontaine-Illusie and Kato, as needed for Nishinou and Siebert's proof of Mikhalkin's tropical curve counting formulas. This latter proof is given in the fourth chapter. The fifth chapter considers the mirror, B-model side, giving recent results of the author showing how tropical geometry can be used to evaluate the oscillatory integrals appearing. The final chapter surveys reconstruction results of the author and Siebert for “integral tropical manifolds.” A complete version of the argument is given in two dimensions.

A co-publication of the AMS and CBMS.

Graduate students and research mathematicians interested in mirror symmetry and tropical geometry.

• Chapters
• Part I. The three worlds
• Chapter 1. The tropics
• Chapter 2. The A- and B-models
• Chapter 3. Log geometry
• Part II. Example: $\mathbb {P}^2$
• Chapter 4. Mikhalkin’s curve counting formula
• Chapter 5. Period integrals
• Part III. The Gross-Siebert program
• Chapter 6. The program and two-dimensional results

• Reviews

• This book is well-written and provides very useful introductory accounts of many aspects of the highly involved subject of mirror symmetry. This book can be extremely helpful to those who want to understand mirror symmetry and the Gross-Siebert program.

Mathematical Reviews
• Requests

Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
Volume: 1142011; 317 pp
MSC: Primary 14; 52;

Tropical geometry provides an explanation for the remarkable power of mirror symmetry to connect complex and symplectic geometry. The main theme of this book is the interplay between tropical geometry and mirror symmetry, culminating in a description of the recent work of Gross and Siebert using log geometry to understand how the tropical world relates the A- and B-models in mirror symmetry.

The text starts with a detailed introduction to the notions of tropical curves and manifolds, and then gives a thorough description of both sides of mirror symmetry for projective space, bringing together material which so far can only be found scattered throughout the literature. Next follows an introduction to the log geometry of Fontaine-Illusie and Kato, as needed for Nishinou and Siebert's proof of Mikhalkin's tropical curve counting formulas. This latter proof is given in the fourth chapter. The fifth chapter considers the mirror, B-model side, giving recent results of the author showing how tropical geometry can be used to evaluate the oscillatory integrals appearing. The final chapter surveys reconstruction results of the author and Siebert for “integral tropical manifolds.” A complete version of the argument is given in two dimensions.

A co-publication of the AMS and CBMS.

Graduate students and research mathematicians interested in mirror symmetry and tropical geometry.

• Chapters
• Part I. The three worlds
• Chapter 1. The tropics
• Chapter 2. The A- and B-models
• Chapter 3. Log geometry
• Part II. Example: $\mathbb {P}^2$
• Chapter 4. Mikhalkin’s curve counting formula
• Chapter 5. Period integrals
• Part III. The Gross-Siebert program
• Chapter 6. The program and two-dimensional results
• This book is well-written and provides very useful introductory accounts of many aspects of the highly involved subject of mirror symmetry. This book can be extremely helpful to those who want to understand mirror symmetry and the Gross-Siebert program.

Mathematical Reviews
Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
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