Corpus ID: 237941143

Abelianization and Quantum Lefschetz for Orbifold Quasimap $I$-Functions

@inproceedings{Webb2021AbelianizationAQ,
  title={Abelianization and Quantum Lefschetz for Orbifold Quasimap \$I\$-Functions},
  author={Rachel Webb},
  year={2021}
}
Let Y be a complete intersection in an affine variety X, with action by a complex reductive group G. Let T ⊂ G be a maximal torus. A character θ of G defines GIT quotients Y / θG and X/ θT . We prove formulas relating the small quasimap Ifunction of Y / θG to that ofX/ θT . When X is a vector space, this provides a completely explicit formula for the small I-function of Y / θG. 

References

SHOWING 1-10 OF 46 REFERENCES
Quantum Witten localization and abelianization for qde solutions
We prove a quantum version of the localization formula of Witten that relates invariants of a git quotient with the equivariant invariants of the action. Using the formula we prove a quantum versionExpand
The Crepant Transformation Conjecture for Toric Complete Intersections
Abstract Let X and Y be K -equivalent toric Deligne–Mumford stacks related by a single toric wall-crossing. We prove the Crepant Transformation Conjecture in this case, fully-equivariantly and inExpand
A Luna étale slice theorem for algebraic stacks
We prove that every algebraic stack, locally of finite type over an algebraically closed field with affine stabilizers, is etale-locally a quotient stack in a neighborhood of a point with a linearlyExpand
A mirror theorem for toric stacks
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 explicitExpand
Some applications of the mirror theorem for toric stacks
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 toricExpand
Orbifold quasimap theory
We extend to orbifolds the quasimap theory of Ciocan-Fontanine and Kim (Adv Math 225(6):3022–3051, 2010; J Geom Phys 75:17–47, 2014) as well as the genus zero wall-crossing results from (Algebr GeomExpand
Mirror symmetry and the classification of orbifold del Pezzo surfaces
We state a number of conjectures that together allow one to classify a broad class of del Pezzo surfaces with cyclic quotient singularities using mirror symmetry. We prove our conjectures in theExpand
Virtual pull-backs
We propose a generalization of Gysin maps for DM-type morphisms of stacks $F\to G$ that admit a perfect relative obstruction theory $E_{F/G}^{\bullet}$, which we call a "virtual pull-back". We proveExpand
Variations on a theme of Grothendieck
Grothendieck and Harder proved that every principal bundle over the projective line with split reductive structure group (and trivial over the generic point) can be reduced to a maximal torus.Expand
On the quantum periods of del Pezzo surfaces with ⅓ (1, 1) singularities
Abstract In earlier joint work with collaborators we gave a conjectural classification of a broad class of orbifold del Pezzo surfaces, using Mirror Symmetry. We proposed that del Pezzo surfaces XExpand
...
1
2
3
4
5
...