Singularities of generalized Richardson varieties

Understand

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 paper, we study the singularities of each type of generalization.