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SUMMER 2015 Type A quiver loci and Schubert varieties
Ryan Kinser, Jenna Rajchgot
J. Commut. Algebra 7(2): 265-301 (SUMMER 2015). DOI: 10.1216/JCA-2015-7-2-265

Abstract

We describe a closed immersion from each representation space of a type $A$ quiver with bipartite (i.e., alternating) orientation to a certain opposite Schubert cell of a partial flag variety. This ``bipartite Zelevinsky map'' restricts to an isomorphism from each orbit closure to a Schubert variety intersected with the above-mentioned opposite Schubert cell. For type $A$ quivers of arbitrary orientation, we give the same result up to some factors of general linear groups.

These identifications allow us to recover results of Bobi\'nski and Zwara; namely, we see that orbit closures of type $A$ quivers are normal, Cohen-Macaulay and have rational singularities. We also see that each representation space of a type $A$ quiver admits a Frobenius splitting for which all of its orbit closures are compatibly Frobenius split.

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Ryan Kinser. Jenna Rajchgot. "Type A quiver loci and Schubert varieties." J. Commut. Algebra 7 (2) 265 - 301, SUMMER 2015. https://doi.org/10.1216/JCA-2015-7-2-265

Information

Published: SUMMER 2015
First available in Project Euclid: 14 July 2015

zbMATH: 1351.14031
MathSciNet: MR3370487
Digital Object Identifier: 10.1216/JCA-2015-7-2-265

Rights: Copyright © 2015 Rocky Mountain Mathematics Consortium

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Vol.7 • No. 2 • SUMMER 2015
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