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The Abelian-Nonabelian Correspondence for $I$-functions

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arxiv 1804.07786 v3 pith:5O5WLJZE submitted 2018-04-20 math.AG math.SG

Rachel Webb This is my paper · ORCID
classification math.AGmath.SG
keywords functionsabelian-nonabeliancorrespondenceformulagrassmannianprovequasimaptheta
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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.

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  1. A Vafa-Intriligator formula for semi-positive quotients of linear spaces

    math.AG 2025-05 conditional novelty 5.0 of 10

    The paper proves Vafa-Intriligator formulas for genus zero quasimap invariants of smooth semi-positive GIT quotients V//G by reducing them to toric computations via abelianization.

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