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Summer 2022 Class groups of open Richardson varieties in the Grassmannian are trivial
Jake Levinson, Kevin Purbhoo
J. Commut. Algebra 14(2): 267-275 (Summer 2022). DOI: 10.1216/jca.2022.14.267

Abstract

We prove that the divisor class group of any open Richardson variety in the Grassmannian is trivial. Our proof uses Nagata’s criterion, localizing the coordinate ring at a suitable set of Plücker coordinates. We prove that these Plücker coordinates are prime elements by showing that the subscheme they define is an open subscheme of a positroid variety. Our results hold over any field and over the integers.

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Jake Levinson. Kevin Purbhoo. "Class groups of open Richardson varieties in the Grassmannian are trivial." J. Commut. Algebra 14 (2) 267 - 275, Summer 2022. https://doi.org/10.1216/jca.2022.14.267

Information

Received: 6 March 2020; Revised: 28 July 2020; Accepted: 31 July 2020; Published: Summer 2022
First available in Project Euclid: 14 July 2022

Digital Object Identifier: 10.1216/jca.2022.14.267

Subjects:
Primary: 14N15

Keywords: class group , positroid , Richardson variety , unique factorization domain

Rights: Copyright © 2022 Rocky Mountain Mathematics Consortium

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Vol.14 • No. 2 • Summer 2022
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