A mirror theorem for toric stacks
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In this paper, a Givental-style mirror theorem for toric Deligne-Mumford stacks X was proved for genus-zero Gromov-Witten invariants.Abstract:
We prove a Givental-style mirror theorem for toric Deligne–Mumford stacks X . This determines the genus-zero Gromov–Witten invariants of X in terms of an explicit hypergeometric function, called the I-function, that takes values in the Chen–Ruan orbifold cohomology of X .read more
Citations
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Journal ArticleDOI
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
On the remodeling conjecture for toric Calabi-Yau 3-orbifolds
TL;DR: In this article, the BKMP Remodeling Conjecture for all genus open-closed orbifolds Gromov-Witten invariants of an arbitrary semi-projective toric Calabi-Yau 3-orbifold relative to an outer framed Aganagic-Vafa Lagrangian brane was proved.
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On the Remodeling Conjecture for Toric Calabi-Yau 3-Orbifolds
TL;DR: In this paper, the BKMP Remodeling Conjecture for all genus open-closed orbifolds Gromov-Witten invariants of an arbitrary semi-projective toric Calabi-Yau 3-orbifold relative to an outer framed Aganagic-Vafa Lagrangian brane was proved.
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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Quantum cohomology and toric minimal model programs
Eduardo Gonzalez,Chris Woodward +1 more
TL;DR: In this paper, a quantum version of the Danilov-Jurkiewicz presentation of the cohomology of a compact toric orbifold with projective coarse moduli space is given.
References
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TL;DR: In this paper, a new cohomology ring for almost complex orbifolds is constructed based on the string theory model in physics, and the key theorem is the associativity of this new ring.
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TL;DR: In this article, Gromov-Witten invariants of a smooth complex Deligne-Mumford stack with a projective coarse moduli space were introduced and proved.
Book ChapterDOI
A Mirror Theorem for Toric Complete Intersections
TL;DR: In this paper, a generalized mirror conjecture for non-negative complete intersections in symplectic toric manifolds has been proved, where the PDE system describing quantum cohomology of such a manifold is expressed in terms of suitable hypergeometric functions.
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Orbifold Gromov-Witten Theory
Weimin Chen Chen,Yongbin Ruan +1 more
TL;DR: In this paper, the notion of good map was introduced and used to establish Gromov-Witten theory for orbifolds, and the good map theory was used to define good map.