Tropical Geometry and Mirror Symmetry

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  • Tropical Geometry and Mirror Symmetry Book Detail

  • Author : Mark Gross
  • Release Date : 2011-01-20
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 338
  • ISBN 13 : 0821852329
  • File Size : 59,59 MB

Tropical Geometry and Mirror Symmetry by Mark Gross PDF Summary

Book Description: 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.

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Tropical Geometry and Mirror Symmetry

Tropical Geometry and Mirror Symmetry

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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

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This volume contains contributions from the NSF-CBMS Conference on Tropical Geometry and Mirror Symmetry, which was held from December 13-17, 2008 at Kansas Sta

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