Moduli Spaces and Related Topics

Organizers：

Xiang He, Chenglong Yu, Dingxin Zhang, Jie Zhou

Speaker：

Qixiao Ma 马骐骁

ShanghaiTech University

Time：

Wed., 15:30-16:30

Oct. 9, 2024

Venue：

C654, Shuangqing Complex Building

清华大学双清综合楼A座 C654

Title:

Torsors of the Jacobians of the generic Fermat curves

Abstract：

Let C/S be the universal family of degree m (m>3) Fermat curve. Then A=Pic^0_{C/S} is an abelian scheme over S. We show that: (1) All torsors of A/S are of the form Pic^d_{C/S}. (2) Passing to the function field, there are uncountably many non-isomorphic torsors of A_k(S). Finally we discuss some partial results on extending the result to M_g.