On smooth toric Richardson varieties

Abstract: Schubert varieties and Richardson varieties are some of the most interesting subvarieties of the full flag varieties. A maximal torus acts on the full flag variety and these subvarieties are stable under the action. Considering the restriction of the moment map on Richardson varieties, we obtain Bruhat interval polytopes. The combinatorics of Bruhat interval polytopes play an important role in studying toric Richardson varieties. In this talk, we consider an interesting family of smooth toric Richardson varieties each element of which is associated with a cubic Bruhat interval polytope, called a toric variety \textit{of Catalan type}. We study the relationship between the isomorphism classes of toric varieties of Catalan type and polygon triangulations. Moreover, we consider the isomorphism classes of toric Schubert varieties which may not be of Catalan type. This talk is based on joint work with Mikiya Masuda and Seonjeong Park.

algebraic geometry

Audience: researchers in the topic

ZAG (Zoom Algebraic Geometry) seminar

Series comments: Description: ZAG seminar

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