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math.AG2019
Class groups of open Richardson varieties in the Grassmannian are trivial
Jake Levinson, Kevin Purbhoo
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…
math.AG2019
A topological proof of the Shapiro-Shapiro conjecture
Jake Levinson, Kevin Purbhoo
We prove a generalization of the Shapiro-Shapiro conjecture on Wronskians of polynomials, allowing the Wronskian to have complex conjugate roots. We decompose the real Schubert cel…