On Chow and Picard groups of Richardson varieties

Abstract

We show that if $\Pi \subseteq G/P$ is a projected Richardson variety, then the degree map $\mathrm{Pic}(\Pi )\to A_1(\Pi {)}^{\vee }$ is injective. Moreover, it is an isomorphism in characteristic zero and in all but finitely many positive characteristics. We conjecture that it is an isomorphism in every characteristic. Our proofs are geometric, using a linear paving, topological properties of klt singularities, and reduction to characteristic zero.

arXiv comment14 pages