The Abelian-Nonabelian Correspondence for $I$-functions

Rachel Webb

The Abelian-Nonabelian Correspondence for $I$-functions

Algebraic Geometry 2021-05-31 v3 Symplectic Geometry

Authors: Rachel Webb

Abstract

We prove the abelian-nonabelian correspondence for quasimap $I$ -functions. That is, if $Z$ is an affine l.c.i. variety with an action by a complex reductive group $G$ , we prove an explicit formula relating the quasimap $I$ -functions of the GIT quotients $Z//_{\theta} G$ and $Z//_{\theta} T$ where $T$ is a maximal torus of $G$ . We apply the formula to compute the $J$ -functions of some Grassmannian bundles on Grassmannian varieties and Calabi-Yau hypersurfaces in them.

Keywords

algebraic group actions quasi-isometry abelian groups

Cite

@article{arxiv.1804.07786,
  title  = {The Abelian-Nonabelian Correspondence for $I$-functions},
  author = {Rachel Webb},
  journal= {arXiv preprint arXiv:1804.07786},
  year   = {2021}
}

Comments

Strengthened the main result include quotients of affine varieties. The paper is almost entirely rewritten

The Abelian-Nonabelian Correspondence for $I$-functions

Abstract

Keywords

Cite

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