Homological Mirror Symmetry and Tropical Geometry
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 ztr...
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| Otros Autores: | , , , , , |
| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
Cham :
Springer International Publishing
2014.
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| Colección: | Lecture Notes of the Unione Matematica Italiana ;
15. Springer eBooks. |
| Acceso en línea: | Conectar con la versión electrónica |
| Ver en Universidad de Navarra: | https://innopac.unav.es/record=b32918689*spi |
| Sumario: | 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 ztropicaly 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 zdegenerationsy of the corresponding algebro-geometric objects. |
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| Descripción Física: | XI, 436 p., 43 il., 18 il. col |
| Formato: | Forma de acceso: World Wide Web. |
| ISBN: | 9783319065144 |
