수학과

1. 연사: 이은정 (충북대학교)

2. 일시: 11월 25일(금) 오후 5~6시

3. 장소: 팔달관 621호

4. 제목: On toric varieties in the flag variety

5. 초록: 

Let $G$ be a simple Lie group and let $B$ be a Borel subgroup. The homogeneous space $G/B$ becomes a smooth projective variety, called the flag variety. The flag variety provides an interesting connection between geometry, topology, representation theory, and combinatorics as is exhibited in the Borel-Weil-Bott theorem, Schubert calculus, and so on. A maximal (complex) torus $T$ acts on the flag variety and there are lots of toric varieties with respect to this torus action. Indeed, the $T$-orbit closure of a point in the flag variety is always a toric variety. One can produce toric Schubert varieties and toric Richardson varieties in this way. In this talk, we study toric varieties in the flag variety, especially the classification of toric Schubert varieties, and we consider how the geometry of toric Schubert varieties is related to a certain combinatorial object, the directed Dynkin diagram. This talk is based on joint work with Mikiya Masuda and Seonjeong Park.

 

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