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Some Applications of the Mirror Theorem for Toric Stacks
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In this article, the mirror theorem for toric Deligne-Mumford stacks was used to compute genus-zero Gromov-Witten invariants of a number of toric orbifolds and gerbes.Abstract:
We use the mirror theorem for toric Deligne-Mumford stacks, proved recently by the authors and by Cheong-Ciocan-Fontanine-Kim, to compute genus-zero Gromov-Witten invariants of a number of toric orbifolds and gerbes. We prove a mirror theorem for a class of complete intersections in toric Deligne-Mumford stacks, and use this to compute genus-zero Gromov-Witten invariants of an orbifold hypersurface.read more
Citations
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Journal ArticleDOI
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.
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
Towards mirror symmetry for varieties of general type
TL;DR: In this article, the mirror of a hypersurface of general type (and more generally varieties of non-negative Kodaira dimension) is described as the critical locus of the zero fibre of a certain Landau-Ginzburg potential.
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.
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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Gromov - witten invariants and quantization of quadratic hamiltonians
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The orbifold Chow ring of toric Deligne-Mumford stacks
TL;DR: In this article, Chen and Ruan developed the theory of toric Deligne-Mumford stacks, which corresponds to a combinatorial object called a stacky fan.
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Quantum Riemann–Roch, Lefschetz and Serre
Tom Coates,Alexander Givental +1 more
TL;DR: In this paper, Mumford's Grothendieck-Riemann-Roch theorem applied to the universal family over the moduli space of stable maps was extended to twisted Gromov-Witten invariants.
Journal ArticleDOI
Using stacks to impose tangency conditions on curves
TL;DR: In this paper, the authors define a Deligne-Mumford stack Xp r which depends on a scheme X, an effective Carrier divisor D C X, and a positive integer r. This construction was known to several mathematicians before they became aware of it, but very little appeared in the literature aside from a brief mention in (AGV, 3.5.
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