Mirror symmetry and Fukaya categories of singular hypersurfaces
نویسندگان
چکیده
We consider a definition of the Fukaya category singular hypersurface proposed by Auroux, given localizing nearby fiber at Seidel's natural transformation, and show that this possesses several desirable properties. Firstly, we prove an A-side analog Orlov's derived Kn\"orrer periodicity theorem showing Auroux' is equivalent to Fukaya-Seidel higher-dimensional Landau-Ginzburg model. Secondly, describe how should imply homological mirror symmetry various large complex structure limits, in context forthcoming work Abouzaid-Auroux Abouzaid-Gross-Siebert.
منابع مشابه
Remarks On A-branes, Mirror Symmetry, And The Fukaya Category
We discuss D-branes of the topological A-model (A-branes), which are believed to be closely related to the Fukaya category. We give string theory arguments which show that A-branes are not necessarily Lagrangian submanifolds in the Calabi-Yau: more general coisotropic branes are also allowed, if the line bundle on the brane is not flat. We show that a coisotropic A-brane has a natural structure...
متن کاملMirror Symmetry, Mirror Map and Applications to Calabi-Yau Hypersurfaces
Mirror Symmetry, Picard-Fuchs equations and instanton corrected Yukawa couplings are discussed within the framework of toric geometry. It allows to establish mirror symmetry of Calabi-Yau spaces for which the mirror manifold had been unavailable in previous constructions. Mirror maps and Yukawa couplings are explicitly given for several examples with two and three moduli.
متن کاملFukaya categories and deformations
Soon after their first appearance [7], Fukaya categories were brought to the attention of a wider audience through the homological mirror conjecture [14]. Since then Fukaya and his collaborators have undertaken the vast project of laying down the foundations, and as a result a fully general definition is available [9, 6]. The task that symplectic geometers are now facing is to make these catego...
متن کاملLectures on Mirror Symmetry, Derived Categories, and D-branes 1. Mirror Symmetry from a Physical Viewpoint
This is an introduction to Homological Mirror Symmetry, derived categories, and topological D-branes aimed at a mathematical audience. In the last lecture we explain why it is necessary to enlarge the Fukaya category with coisotropic A-branes and discuss how to extend the definition of Floer homology to such objects. These lectures were delivered at IPAM, March 2003, as part of a program on Sym...
متن کاملMirror Symmetry for Toric Branes on Compact Hypersurfaces
We use toric geometry to study open string mirror symmetry on compact Calabi–Yau manifolds. For a mirror pair of toric branes on a mirror pair of toric hypersurfaces we derive a canonical hypergeometric system of differential equations, whose solutions determine the open/closed string mirror maps and the partition functions for spheres and discs. We define a linear sigma model for the brane geo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2022
ISSN: ['1857-8365', '1857-8438']
DOI: https://doi.org/10.1016/j.aim.2021.108116