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Mathematics > Algebraic Geometry

arXiv:1804.07786 (math)
[Submitted on 20 Apr 2018 (v1), last revised 28 May 2021 (this version, v3)]

Title:The Abelian-Nonabelian Correspondence for $I$-functions

Authors:Rachel Webb
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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.
Comments: Strengthened the main result include quotients of affine varieties. The paper is almost entirely rewritten
Subjects: Algebraic Geometry (math.AG); Symplectic Geometry (math.SG)
MSC classes: 14L30, 14N35, 14D23
Cite as: arXiv:1804.07786 [math.AG]
  (or arXiv:1804.07786v3 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1804.07786

Submission history

From: Rachel Webb [view email]
[v1] Fri, 20 Apr 2018 18:27:33 UTC (24 KB)
[v2] Thu, 25 Oct 2018 13:36:47 UTC (26 KB)
[v3] Fri, 28 May 2021 13:12:00 UTC (63 KB)
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