• Corpus ID: 235212528

Local mirror symmetry via SYZ

@inproceedings{Gammage2021LocalMS,
  title={Local mirror symmetry via SYZ},
  author={Benjamin Gammage},
  year={2021}
}
In this note, we explain how mirror symmetry for basic local models in the Gross-Siebert program can be understood through the non-toric blowup construction described by Gross-Hacking-Keel. This is part of a program to understand the symplectic geometry of affine cluster varieties through their SYZ fibrations. 
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References

SHOWING 1-10 OF 32 REFERENCES

Homological Mirror Symmetry for local SYZ singularities

Gross and Siebert identified a class of singular Lagrangian torus fibrations which arise when smoothing toroidal degenerations, and which come in pairs that are related by mirror symmetry. We…

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  • V. Shende
  • Mathematics
    Comptes Rendus. Mathématique
  • 2022
The Cox construction presents a toric variety as a quotient of affine space by a torus. The category of coherent sheaves on the corresponding stack thus has an evident description as invariants in a…

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…

Mirror symmetry for Berglund-H\"ubsch Milnor fibers.

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…

Lagrangian Torus Fibrations and Homological Mirror Symmetry for the Conifold

We discuss homological mirror symmetry for the conifold from the point of view of the Strominger–Yau–Zaslow conjecture.

Wall-crossing for toric mutations

This note explains how to deduce the wall-crossing formula for toric mutations established by Pascaleff-Tonkonog from the perverse schober of the corresponding local Landau-Ginzburg model. Along the…

The nonequivariant coherent-constructible correspondence for toric surfaces

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…

Homological mirror symmetry at large volume

. A typical large complex-structure limit for mirror symmetry consists of toric varieties glued to each other along their toric boundaries. Here we construct the mirror large volume limit space as a…

Lagrangian fibrations on blowups of toric varieties and mirror symmetry for hypersurfaces

We consider mirror symmetry for (essentially arbitrary) hypersurfaces in (possibly noncompact) toric varieties from the perspective of the Strominger-Yau-Zaslow (SYZ) conjecture. Given a hypersurface…

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…