Homological Mirror Symmetry and Tropical Geometry (Paperback, 2014)

The relationship between Tropical Geometry and Mirror Symmetry goes back to the work of Kontsevich and Y. Soibelman (2000), who applied methods of non-archimedean geometry (in particular, tropical curves) to Homological Mirror Symmetry. In combination with the subsequent work of Mikhalkin on the "tropical" approach to Gromov-Witten theory and the work of Gross and Siebert, Tropical Geometry has now become a powerful tool. Homological Mirror Symmetry is the area of mathematics concentrated around several categorical equivalences connecting symplectic and holomorphic (or algebraic) geometry. The central ideas first appeared in the work of Maxim Kontsevich (1993). Roughly speaking, the subject can be approached in two ways: either one uses Lagrangian torus fibrations of Calabi-Yau manifolds (the so-called Strominger-Yau-Zaslow picture, further developed by Kontsevich and Soibelman) or one uses Lefschetz fibrations of symplectic manifolds (suggested by Kontsevich and further developed by Seidel). Tropical Geometry studies piecewise-linear objects which appear as "degenerations" of the corresponding algebro-geometric objects.

General

Imprint:	Springer International Publishing AG
Country of origin:	Switzerland
Series:	Lecture Notes of the Unione Matematica Italiana, 15
Release date:	October 2014
First published:	2014
Editors:	Ricardo Castano-Bernard • Fabrizio Catanese • Maxim Kontsevich • Tony Pantev • Yan Soibelman • Ilia Zharkov
Dimensions:	235 x 155 x 25mm (L x W x T)
Format:	Paperback
Pages:	436
Edition:	2014
ISBN-13:	978-3-319-06513-7
Categories:	Books > Science & Mathematics > Mathematics > Geometry > Differential & Riemannian geometry Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry
LSN:	3-319-06513-0
Barcode:	9783319065137

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