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

2016/03/30 by Roberto Fringuelli, Fringuelli, Roberto, Roberto Pirisi +1
Mathematics · Social Sciences · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Vietnamese History and Culture Studies

paper · pdf · doi:10.48550/arxiv.1603.09190

openalex publication_date 2016/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the Picard group of the universal abelian variety over the moduli\nstack mathscr A_g,n of principally polarized abelian varieties over\n\ℂ with a symplectic principal level n-structure. We then prove\nthat over \ℂ the statement of the Franchetta conjecture holds in a\nsuitable form for mathscr A_g,n.\n

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