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.
General
Imprint: |
American Mathematical Society
|
Country of origin: |
United States |
Series: |
CBMS Regional Conference Series in Mathematics |
Release date: |
2011 |
First published: |
2011 |
Authors: |
Mark Gross
|
Dimensions: |
254 x 178mm (L x W) |
Format: |
Paperback
|
Pages: |
317 |
ISBN-13: |
978-0-8218-5232-3 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
Geometry >
Algebraic geometry
|
LSN: |
0-8218-5232-9 |
Barcode: |
9780821852323 |
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