Speaker: Qixiao Ma (ShanghaiTech University)
Abstract: Let $C/S$ be the universal family of degree-$m$ plane Fermat curves. The relative Jacobian, denoted by $Jac_{C/S}$, is an abelian scheme over $S$. (1) We explicitly classify all torsors of $Jac_{C/S}$, and show that there are only $m$ or $m/2$ of them, according to the parity of $m$. (2) On the other hand, we show that there are uncountably many non-isomorphic torsors of $A_K$ over the function field $K=f.f(S)$. (3) Finally we generalize the discussion to $M_g$ and give partial results.
Time: 10:00-11:30 a.m., Wednesday, Nov. 13, 2024
Location: Room 1210 at SIMIS, Block A, No. 657 Songhu Road, Yangpu District, Shanghai
English 
简体中文