Mirror symmetry for Berglund-H\"ubsch Milnor fibers.
@article{Gammage2020MirrorSF, title={Mirror symmetry for Berglund-H\"ubsch Milnor fibers.}, author={Benjamin Gammage}, journal={arXiv: Symplectic Geometry}, year={2020} }
We prove the conjecture of Yank{\i} Lekili and Kazushi Ueda on homological mirror symmetry for Milnor fibers of Berglund-H\"ubsch invertible polynomials. The proof proceeds as usual by calculating the "very affine" Fukaya category and then deforming it, relating the local categorical deformations to a calculation of David Nadler. The proof may be understood as a basic calculation in the deformation theory of perverse schobers.
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References
SHOWING 1-10 OF 64 REFERENCES
Mirror symmetry for very affine hypersurfaces
- Mathematics
- 2017
We show that the category of coherent sheaves on the toric boundary divisor of a smooth quasiprojective DM toric stack is equivalent to the wrapped Fukaya category of a hypersurface in a complex…
Homological mirror symmetry for hypertoric varieties II
- Mathematics
- 2018
In this paper, we prove a homological mirror symmetry equivalence for pairs of multiplicative hypertoric varieties, and we calculate monodromy autoequivalences of these categories by promoting our…
Homological mirror symmetry for the genus two curve
- Mathematics
- 2008
Katzarkov has proposed a generalization of Kontsevich's mirror symmetry conjecture, covering some varieties of general type. We prove a version of this conjecture in the simplest example, relating…
Homological mirror symmetry for invertible polynomials in two variables
- MathematicsQuantum Topology
- 2022
In this paper we give a proof of homological mirror symmetry for two variable invertible polynomials, where the symmetry group on the $B$-side is taken to be maximal. The proof involves an explicit…
Homogeneous coordinate rings and mirror symmetry for toric varieties
- Mathematics
- 2006
Given a smooth toric variety X and an ample line bundle O(1), we construct a sequence of Lagrangian submanifolds of (C^*)^n with boundary on a level set of the Landau-Ginzburg mirror of X. The…
Fukaya category for Landau-Ginzburg orbifolds
- Mathematics
- 2020
For a weighted homogeneous polynomial and a choice of a diagonal symmetry group, we define a new Fukaya category for a Landau-Ginzburg orbifold (of Fano or Calabi-Yau type). The construction is based…
The nonequivariant coherent-constructible correspondence for toric stacks
- MathematicsDuke Mathematical Journal
- 2020
We prove the nonequivariant coherent-constructible correspondence conjectured by Fang-Liu-Treumann-Zaslow in the case of toric surfaces. Our proof is based on describing a semi-orthogonal…
Microlocal Category for Weinstein Manifolds via the h-Principle
- MathematicsPublications of the Research Institute for Mathematical Sciences
- 2021
On a Weinstein manifold, we define a constructible co/sheaf of categories on the skeleton. The construction works with arbitrary coefficients, and depends only on the homotopy class of a section of…
Covariantly functorial wrapped Floer theory on Liouville sectors
- MathematicsPublications mathématiques de l'IHÉS
- 2019
We introduce a class of Liouville manifolds with boundary which we call Liouville sectors. We define the wrapped Fukaya category, symplectic cohomology, and the open-closed map for Liouville sectors,…
Microlocal Morse theory of wrapped Fukaya categories
- Mathematics
- 2018
Consider on the one hand the partially wrapped Fukaya category of a cotangent bundle stopped at an appropriately stratifiable singular isotropic. Consider on the other hand the derived category of…