Homological Mirror Symmetry and Tropical Geometry

Ricardo Castano-Bernard (u. a.)

ISBN 10: 3319065130 / ISBN 13: 9783319065137

Published by Springer, 2014

About this Item

Homological Mirror Symmetry and Tropical Geometry | Ricardo Castano-Bernard (u. a.) | Taschenbuch | Lecture Notes of the Unione Matematica Italiana | xi | Englisch | 2014 | Springer | EAN 9783319065137 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.

Seller Inventory # 105210540

Bibliographic Details

• Title: Homological Mirror Symmetry and Tropical Geometry
• Publisher: Springer
• Publication Date: 2014
• Language: English
• ISBN 10: 3319065130
• ISBN 13: 9783319065137
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 25D millimeters 235 millimeters width by 155 millimeters height by 25 millimeters depth
• Weight: 680 grams
• Seller catalogs:
  • Bücher

About this title

Synopsis

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.