Homological Mirror Symmetry and Tropical Geometry

Nonfiction, Science & Nature, Mathematics, Geometry
Cover of the book Homological Mirror Symmetry and Tropical Geometry by , Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: ISBN: 9783319065144
Publisher: Springer International Publishing Publication: October 7, 2014
Imprint: Springer Language: English
Author:
ISBN: 9783319065144
Publisher: Springer International Publishing
Publication: October 7, 2014
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer International Publishing

Cover of the book Performability in Internet of Things by
Cover of the book Directed Polymers in Random Environments by
Cover of the book Religion and Development in the Global South by
Cover of the book Advances in Neural Networks - ISNN 2017 by
Cover of the book Modelling and Simulation of Diffusive Processes by
Cover of the book Urogenital Pain by
Cover of the book Pesky Essays on the Logic of Philosophy by
Cover of the book Fundamentals of Computer Architecture and Design by
Cover of the book From Post-Democracy to Neo-Democracy by
Cover of the book Assortment and Merchandising Strategy by
Cover of the book Excel 2016 for Social Science Statistics by
Cover of the book Global Innovation of Teaching and Learning in Higher Education by
Cover of the book Curricula for Sustainability in Higher Education by
Cover of the book Friction Material Composites by
Cover of the book Pericyte Biology in Disease by
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy