Homological Mirror Symmetry and Tropical Geometry

Homological Mirror Symmetry and Tropical Geometry

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Cod produs/ISBN: 9783319065137

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Editura: Springer

Limba: Engleza

Nr. pagini: 452

Coperta: Paperback

Dimensiuni: 15.5 x 2.7 x 23.5 cm

An aparitie: 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.


Springer
An aparitie 2014
Autor Ricardo Castano-Bernard , Fabrizio Catanese
Dimensiuni 15.5 x 2.7 x 23.5 cm
Editura Springer
Format Paperback
ISBN 9783319065137
Limba Engleza
Nr pag 452

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