Torsors of the Jacobians of the universal Fermat curves

2024/08/13 by Ma, Qixiao
#14F22 #14G27 #14H10 #Algebraic Geometry (math.AG) #FOS: Mathematics #General Topology (math.GN) #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2408.06962

Abstract

Let m≥3 be an integer. We show that every torsor of the Jacobian of the universal family of degree-m Fermat curve is necessarily a connected component of the Picard scheme. We show that the Jacobian of the generic degree-m Fermat curve has uncountably many non-isomorphic torsors. We give some results towards the Franchetta type problem for torsors of the Jacobian of the universal family of genus-g curves over M_g.

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