Class groups of open Richardson varieties in the Grassmannian are trivial
Algebraic Geometry
2019-08-09 v1
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 Pl\"ucker coordinates. We prove that these Pl\"ucker 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.
Keywords
Cite
@article{arxiv.1908.02925,
title = {Class groups of open Richardson varieties in the Grassmannian are trivial},
author = {Jake Levinson and Kevin Purbhoo},
journal= {arXiv preprint arXiv:1908.02925},
year = {2019}
}
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10 pages