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 Public Health Intelligence by
Cover of the book E-Learning in the Middle East and North Africa (MENA) Region by
Cover of the book Collectivity and Power on the Internet by
Cover of the book Why Bank Panics Matter by
Cover of the book Adaptive Water Management by
Cover of the book Conventional Water Resources and Agriculture in Egypt by
Cover of the book Privacy and Identity Management. Fairness, Accountability, and Transparency in the Age of Big Data by
Cover of the book Modelling and Implementation of Complex Systems by
Cover of the book Corporate Performance by
Cover of the book Critical Care Nutrition Therapy for Non-nutritionists by
Cover of the book Computing and Combinatorics by
Cover of the book Integrated Early Childhood Behavioral Health in Primary Care by
Cover of the book The Euclidean Matching Problem by
Cover of the book Optimizing Hospital-wide Patient Scheduling by
Cover of the book New Trends in Analysis and Interdisciplinary Applications 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