- 代数讨论班

The number of full exceptional collections modulo spherical twists for extended Dynkin quivers

组织者

邱宇

演讲者

Takumi OKANI

时间

2023年09月15日 11:20 至 12:20

地点

A3-1-301

摘要

For a Dynkin quiver, Obaid—Nauman—Shammakh—Fakieh—Ringel gave a counting formula for the number of full exceptional collections in the derived category. This number is equal to the number of distinguished bases of vanishing cycles (up to sign) for ADE singularities. On the other hand, Deligne showed the number of distinguished bases coincides with the degree of Lyashko—Looijenga map for simple singularities. In this talk, I will give a formula of the number for full exceptional collections modulo spherical twists for extended Dynkin quivers. The formula implies that the number of full exceptional collections in the derived category of an orbifold projective line is equal to the degree of Lyashko—Looijenga map of the orbifold projective line. If time permits, I will also explain a conjectural relationship between this number and the space of Bridgeland stability conditions. This talk is based on a joint work with Yuuki Shiraishi and Atsushi Takahashi.