A mirror theorem for toric stacks

By Tom Coates, Alessio Corti, H. Iritani, Hsian-Hua Tseng. Compositio Mathematica, 2013

107 citations recorded by the source corpus.

We prove a Givental-style mirror theorem for toric Deligne–Mumford stacks ${\mathcal{X}}$. This determines the genus-zero Gromov–Witten invariants of ${\mathcal{X}}$ in terms of an explicit hypergeometric function, called the $I$-function, that takes values in the Chen–Ruan orbifold cohomology of ${\mathcal{X}}$.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/9e9b3ec20e9f410ff6fdf9afb6d8edc6aa63fd38

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

Citations in the corpus

QUANTUM KIRWAN MORPHISM AND GROMOV-WITTEN INVARIANTS OF QUOTIENTS I (2012, background): “To explain the gauged Gromov-Witten potential, recall that the equivariant cohomology of a G-space X is the cohomology of the homotopy quotient XG = EG ×G X where EG → BG is a universal G-bundle.”
Mirror symmetry and the classification of orbifold del Pezzo surfaces (2015, methodology): “One can see this already in the case of X = P(1, 1, 6), where the quantum period can be computed using the Mirror Theorem for toric Deligne– Mumford stacks [10, 12], and the corresponding maximally-mutable Laurent polynomial is f = x+y+xy+a1y +a2y +a3y −3 where a1, a2, and a3 are parameters.”
Orbifold quasimap theory (2014, methodology): “X) with H∗ T(IµX) by the pullback ∗. (Of course, the interpretation of the mirror map as a generating series of quasimap invariants is new.) Part (2) of the Corollary is precisely the main result of [13]. Note that the notion of “S-extended I-function” from [13] corresponds in our terminology to the”
The Crepant Transformation Conjecture for Toric Complete Intersections (2014, methodology): “We use the Mirror Theorem for toric Deligne– Mumford stacks [26, 30] to construct a global equivariant quantum connection over (a certain part of) the secondary toric variety for X±; this gives an analytic continuation of the equivariant quantum connections for X+ and X−.”