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Fall 2021 Singularities of zero sets of semi-invariants for quivers
András Cristian Lőrincz
J. Commut. Algebra 13(3): 361-380 (Fall 2021). DOI: 10.1216/jca.2021.13.361

Abstract

Let Q be a quiver with dimension vector α prehomogeneous under the action of the product of general linear groups GL(α) on the representation variety Rep(Q,α). We study geometric properties of zero sets of semi-invariants of this space. It is known that for large numbers N, the nullcone in Rep(Q,Nα) becomes a complete intersection. First, we show that it also becomes reduced. Then, using Bernstein–Sato polynomials, we discuss some criteria for zero sets to have rational singularities. In particular, we show that for Dynkin quivers codimension 1 orbit closures have rational singularities.

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András Cristian Lőrincz. "Singularities of zero sets of semi-invariants for quivers." J. Commut. Algebra 13 (3) 361 - 380, Fall 2021. https://doi.org/10.1216/jca.2021.13.361

Information

Received: 1 January 2017; Revised: 7 June 2018; Accepted: 3 March 2019; Published: Fall 2021
First available in Project Euclid: 18 January 2022

Digital Object Identifier: 10.1216/jca.2021.13.361

Subjects:
Primary: 11S90 , 14F10 , 16G20
Secondary: 13A50 , 14B05

Keywords: Bernstein–Sato polynomials , nullcones , prehomogeneous vector spaces , quivers , rational singularities , semi-invariants

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium

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Vol.13 • No. 3 • Fall 2021
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