BIMSA > Algebra Seminar The number of full exceptional collections modulo spherical twists for extended Dynkin quivers
The number of full exceptional collections modulo spherical twists for extended Dynkin quivers
Organizer
Yu Qiu
Speaker
Takumi OKANI
Time
Friday, September 15, 2023 11:20 AM - 12:20 PM
Venue
A3-1-301
Abstract
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.