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 Gottlieb and Whitehead Center Groups of Spheres, Projective and Moore Spaces by
Cover of the book Chinese Agriculture in the 1930s by
Cover of the book Materials Research for Manufacturing by
Cover of the book Complex System Modelling and Control Through Intelligent Soft Computations by
Cover of the book Monitoring the Nervous System for Anesthesiologists and Other Health Care Professionals by
Cover of the book Fixed Point Theory in Modular Function Spaces by
Cover of the book Essays on Hilda Hilst by
Cover of the book Intracellular Delivery III by
Cover of the book Design Thinking Research by
Cover of the book Difficult Decisions in Vascular Surgery by
Cover of the book Database Systems for Advanced Applications by
Cover of the book Environmental Load Factors and System Strength Evaluation of Offshore Jacket Platforms by
Cover of the book Data Integration in the Life Sciences by
Cover of the book Painlevé III: A Case Study in the Geometry of Meromorphic Connections by
Cover of the book Portfolio Selection Using Multi-Objective Optimisation 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