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• W2011208855 abstract "Richardson varieties play an important role in intersection theory and in the geometric interpretation of the Littlewood–Richardson Rule for flag varieties. We discuss three natural generalizations of Richardson varieties which we call projection varieties, intersection varieties, and rank varieties. In many ways, these varieties are more fundamental than Richardson varieties and are more easily amenable to inductive geometric constructions. In this article, we study the singularities of each type of generalization. Like Richardson varieties, projection varieties are normal with rational singularities. We also study in detail the singular loci of projection varieties in Type A Grassmannians. We use Kleiman's Transversality Theorem to determine the singular locus of any intersection variety in terms of the singular loci of Schubert varieties. This is a generalization of a criterion for any Richardson variety to be smooth in terms of the nonvanishing of certain cohomology classes which has been known by some experts in the field, but we don't believe has been published previously." @default.
• W2011208855 created "2016-06-24" @default.
• W2011208855 creator A5081919884 @default.
• W2011208855 creator A5090924793 @default.
• W2011208855 date "2012-04-01" @default.
• W2011208855 modified "2023-10-14" @default.
• W2011208855 title "Singularities of Generalized Richardson Varieties" @default.
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• W2011208855 doi "https://doi.org/10.1080/00927872.2011.551903" @default.
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