Torsors under the universal Jacobian over M_g

2026/07/19 by Qixiao Ma
Mathematics · #math.AG #msc:14D23 #msc:14F22 #msc:14H10 #msc:57K20

paper · pdf

11 pages

arxiv created 2026/07/29 · arxiv updated 2026/07/30

Abstract

We consider the universal family of smooth genus-g curves over ℂ. We show that for g≥4, every torsor under the relative Jacobian is isomorphic to a connected component of the relative Picard scheme. As a byproduct, we show that Br(M_3,1)=ℤ/2ℤ over ℂ and H₂(Γ_3,1,ℤ)=ℤ/2ℤ, pinning down the torsion subgroup in \cite[Theorem 1.2]zbMATH01991000.

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