Equivariant approach to weighted projective curves

组织者 Organizer:Ruan Shiquan
时间 Time: Wed 15:00-17:00,2021 - 5 - 17
地点 Venue:Lecture Hall, Jin Chun Yuan West Bldg.

摘要 Abstract

In this talk, we will introduce the group actions on the category of coherent sheaves over weighted projective lines. We show that the equivariant category with respect to certain finite group action is equivalent to the category of coherent sheaves over a weighted projective curve, where the genus of the underlying smooth projective curve and the weight data are given by explicit formulas. Moreover, a trichotomy result for all such equivariant relations will be given. This equivariant approach provides an effective way to investigate smooth projective curves via weighted projective lines. As an application, we give a description for the category of coherent sheaves over a hyperelliptic curve of arbitrary genus. Links to smooth projective curves of genus 2 and also to Arnold's exceptional unimodal singularities are also established. This is joint work with Qiang Dong and Hongxia Zhang.