A mirror theorem for the mirror quintic
Yuan-Pin Lee,Mark Shoemaker +1 more
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In this paper, it was shown that the B model of the Fermat quintic threefold is equivalent to the A model of its mirror, and hence established the mirror symmetry as a true duality.Abstract:
The celebrated Mirror theorem states that the genus zero part of the A model (quantum cohomology, rational curves counting) of the Fermat quintic threefold is equivalent to the B model (complex deformation, variation of Hodge structure) of its mirror dual orbifold. In this article, we establish a mirror-dual statement. Namely, the B model of the Fermat quintic threefold is shown to be equivalent to the A model of its mirror, and hence establishes the mirror symmetry as a true duality. 14N35; 53D45read more
Citations
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A Mirror Theorem for Toric Stacks
TL;DR: In this article, a Givental-style mirror theorem for toric Deligne-Mumford stacks X was proved for genus-zero Gromov-Witten invariants.
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The Crepant Transformation Conjecture for Toric Complete Intersections
TL;DR: The Mirror Theorems for toric Deligne-Mumford stacks and toric complete intersections were proved in this article, and the Mellin-Barnes method for analytic continuation of hypergeometric functions.
Journal ArticleDOI
A mirror theorem for toric stacks
TL;DR: In this paper, a Givental-style mirror theorem for toric Deligne-Mumford stacks X was proved for genus-zero Gromov-Witten invariants.
Journal ArticleDOI
Gross fibrations, SYZ mirror symmetry, and open Gromov–Witten invariants for toric Calabi–Yau orbifolds
TL;DR: In this article, a non-toric Lagrangian torus fibration on a toric Calabi-Yau (CY) orbifold, called the Gross fibration, was constructed using the Strominger and Yau-Zaslow recipe.
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A Landau-Ginzburg/Calabi-Yau correspondence for the mirror quintic
Nathan Priddis,Mark Shoemaker +1 more
TL;DR: In this article, a version of the Landau-Ginzburg/Calabi-Yau correspondence for the mirror quintic was shown to be equivalent to the Gromov-Witten theory of the Fermat quintic polynomial.
References
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A Pair of Calabi-Yau manifolds as an exactly soluble superconformal theory
TL;DR: In this paper, the prepotentials and geometry of the moduli spaces for a Calabi-Yau manifold and its mirror were derived and all the sigma model corrections to the Yukawa couplings and moduli space metric were obtained.
Journal Article
Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties
TL;DR: In this article, it was shown that there exists an isomorphism between two conformal field theories corresponding to Calabi-Yau varieties from two families of algebraic compactifications of affine hypersurfaces.
Book
Mirror symmetry and algebraic geometry
David A. Cox,Sheldon Katz +1 more
TL;DR: The quintic threefold Toric geometry Mirror symmetry constructions Hodge theory and Yukawa couplings Moduli spaces Gromov-Witten invariants Quantum cohomology Localization Quantum differential equations The mirror theorem Conclusion Singular varieties Physical theories Bibliography Index as mentioned in this paper
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Localization of virtual classes
T. Graber,Rahul Pandharipande +1 more
TL;DR: In this paper, the authors prove a localization formula for virtual fundamental classes in the context of torus equivariant perfect obstruction theories, where the higher genus Gromov-Witten invariants of projective space are expressed as graph sums of tautological integrals over moduli spaces of stable pointed curves.