• Corpus ID: 225102867

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

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

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

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

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

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

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

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

  • V. Shende
  • Mathematics
    Publications 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

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

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
...