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arXiv · 1603.09190

The Picard group of the universal abelian variety and the Franchetta conjecture for abelian varieties

Roberto Fringuelli·Roberto Pirisi
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Abstract

We compute the Picard group of the universal abelian variety over the moduli stack $\mathscr A_{g,n}$ of principally polarized abelian varieties over $\mathbb{C}$ with a symplectic principal level $n$-structure. We then prove that over $\mathbb{C}$ the statement of the Franchetta conjecture holds in a suitable form for $\mathscr A_{g,n}$.

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Roberto Fringuelli, Roberto Pirisi. 2016-03-30. The Picard group of the universal abelian variety and the Franchetta conjecture for abelian varieties. https://arxiv.org/abs/1603.09190

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