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Geometry and Dynamics Seminar
The number of full exceptional collections for orbifold projective lines
The number of full exceptional collections for orbifold projective lines
Organizer
Speaker
Takumi Otani
Time
Wednesday, April 17, 2024 1:30 PM - 3:30 PM
Venue
A3-1-101
Online
Zoom 928 682 9093
(BIMSA)
Abstract
The derived category of an orbifold projective line with positive Euler characteristic is equivalent to the one of an extended Dynkin quiver. For a Dynkin quiver, Obaid—Nauman—Shammakh—Fakieh—Ringel gave a counting formula for the number of full exceptional collections in the derived category. The number coincides with the degree of the Lyashko—Looijenga map for an ADE singularity. The equality of these numbers hints a consistency in some problems in Bridgeland stability conditions and mirror symmetry. In this talk, I will give a formula for the number of full exceptional collections for an orbifold projective line, which can be regarded as a generalization for Dynkin cases. Based on mirror symmetry, I will explain the relationship between the number and the degree of the Lyashko—Looijenga map for the orbifold projective line. This talk is based on a joint work with Yuuki Shiraishi and Atsushi Takahashi.