Birationality of Berglund–Hübsch–Krawitz Mirrors

@article{Shoemaker2014BirationalityOB,
  title={Birationality of Berglund–H{\"u}bsch–Krawitz Mirrors},
  author={M. Shoemaker},
  journal={Communications in Mathematical Physics},
  year={2014},
  volume={331},
  pages={417-429}
}
  • M. Shoemaker
  • Published 2014
  • Physics, Mathematics
  • Communications in Mathematical Physics
We investigate a multiple mirror phenomenon arising from Berglund–Hübsch–Krawitz mirror symmetry. We prove that the different mirror Calabi–Yau orbifolds which arise in this context are in fact birational to one another. 
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References

SHOWING 1-10 OF 10 REFERENCES
Berglund-Hübsch Mirror Symmetry via Vertex Algebras
We give a vertex algebra proof of the Berglund-Hübsch duality of nondegenerate invertible potentials. We suggest a way to unify it with the Batyrev-Borisov duality of reflexive Gorenstein cones.
LG/CY correspondence: the state space isomorphism
We prove the classical mirror symmetry conjecture for the mirror pairs constructed by Berglund, H\"ubsch, and Krawitz. Our main tool is a cohomological LG/CY correspondence which provides aExpand
A generalized construction of mirror manifolds
Abstract We generalize the known method for explicit construction of mirror pairs of (2,2)-superconformal field theories, using the formalism of Landau-Ginzburg orbifolds. Geometrically, theseExpand
FJRW rings and Landau-Ginzburg Mirror Symmetry
In this article, we study the Berglund--H\"ubsch transpose construction W^T for invertible quasihomogeneous potential W. We introduce the dual group G^T and establish the state space isomorphismExpand
Mirror symmetry and algebraic geometry
Introduction The quintic threefold Toric geometry Mirror symmetry constructions Hodge theory and Yukawa couplings Moduli spaces Gromov-Witten invariants Quantum cohomology Localization QuantumExpand
Duality for toric Landau-Ginzburg models
We introduce a duality construction for toric Landau-Ginzburg models, applicable to complete intersections in toric varieties via the sigma model / Landau-Ginzburg model correspondence. ThisExpand
The Witten equation, mirror symmetry and quantum singularity theory
For any non-degenerate, quasi-homogeneous hypersurface singularity, we describe a family of moduli spaces, a virtual cycle, and a corresponding cohomological field theory associated to theExpand
Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
We consider families ${\cal F}(\Delta)$ consisting of complex $(n-1)$-dimensional projective algebraic compactifications of $\Delta$-regular affine hypersurfaces $Z_f$ defined by Laurent polynomialsExpand
Dual cones and mirror symmetry for generalized Calabi-Yau manifolds