Equivariant approach to weighted projective curves
Equivariant approach to weighted projective curves
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DOI：
10.1016/j.jalgebra.2022.05.032
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Hongxia Zhang
中科院分区：
文献类型：
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作者：
Qiang Dong;Shiquan Ruan;Hongxia Zhang
We investigate 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 quivariant relations. 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.
