2020/01/07 by Sara Torelli, Torelli, Sara
Mathematics · #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #math.AG
paper · pdf · doi:10.48550/arxiv.2001.02113
arxiv created 2020/01/07 · openalex publication_date 2020/01/07 · arxiv updated 2020/01/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the paper we consider the Jacobian locus Jg and the Prym locus Pg+1, in the moduli space Ag of principally polarized abelian varieties of dimension g, for g≥ 7, and we study the extrinsic geometry of Jg⊂ Pg+1, under the inclusion provided by the theory of generalized Prym varieties as introduced by Beauville. More precisely, we study certain geodesic curves with respect to the Siegel metric of Ag, starting at a Jacobian variety [JC]∈ Ag of a curve [C]∈ Mg and with direction ζ∈ T[JC]Jg. We prove that for a general JC, any geodesic of this kind is not contained in Jg and even in Pg+1, if ζ has rank k<\Cliff C-3, where \Cliff C denotes the Clifford index of C.