A resolution of singularities for Drinfeld’s compactification by stable maps

Campbell, Justin

doi:10.1090/jag/727

Author: Justin Campbell
Journal: J. Algebraic Geom. 28 (2019), 153-167
DOI: https://doi.org/10.1090/jag/727
Published electronically: October 11, 2018
MathSciNet review: 3875364
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Abstract | References | Additional Information

Abstract: Drinfeld’s relative compactification plays a basic role in the theory of automorphic sheaves, and its singularities encode representation-theoretic information in the form of intersection cohomology. We introduce a resolution of singularities consisting of stable maps from nodal deformations of the curve into twisted flag varieties. As an application, we prove that the twisted intersection cohomology sheaf on Drinfeld’s compactification is universally locally acyclic over the moduli stack of $G$-bundles at points sufficiently antidominant relative to their defect.

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Additional Information

Justin Campbell
Affiliation: Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138
Address at time of publication: Department of Mathematics, California Institute of Technology, 1200 E. California Boulevard, Pasadena, California 91125
MR Author ID: 1198566
Email: jcampbell@caltech.edu

Received by editor(s): April 11, 2017
Received by editor(s) in revised form: May 28, 2018
Published electronically: October 11, 2018
Article copyright: © Copyright 2018 University Press, Inc.