Abstract
We prove that the divisor class group of any open Richardson variety in the Grassmannian is trivial. Our proof uses Nagataâs criterion, localizing the coordinate ring at a suitable set of PlĂŒcker coordinates. We prove that these PlĂŒcker 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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