In this talk I will introduce 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, we obtain a trichotomy result for all such equivariant relations. As an application, we give a description for the category of coherent sheaves over a hyperelliptic curve of arbitrary genus.

会议密码：2021