On the Jacobian locus in the Prym locus and geodesics

Sara Torelli

doi:10.1515/advgeom-2021-0037

Details

Original language	English
Pages (from-to)	431-444
Number of pages	14
Journal	Advances in Geometry
Volume	22
Issue number	3
Early online date	18 Apr 2021
Publication status	Published - 26 Jul 2022

Abstract

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.
Subjects: Algebraic Geometry (math.AG)
Cite as: arXiv:2001.02113 [math.AG]
(or arXiv:2001.02113v1 [math.AG] for this version)

Keywords

math.AG, geodesics, Prym locus, Jacobian locus, Moduli space of curves and abelian varieties, admissible coverings, generalized Prym varieties

ASJC Scopus subject areas

Mathematics(all)
Geometry and Topology

Cite this

On the Jacobian locus in the Prym locus and geodesics. / Torelli, Sara.
In: Advances in Geometry, Vol. 22, No. 3, 26.07.2022, p. 431-444.

Research output: Contribution to journal › Article › Research › peer review

Torelli, S 2022, 'On the Jacobian locus in the Prym locus and geodesics', Advances in Geometry, vol. 22, no. 3, pp. 431-444. https://doi.org/10.1515/advgeom-2021-0037

Torelli, S. (2022). On the Jacobian locus in the Prym locus and geodesics. Advances in Geometry, 22(3), 431-444. https://doi.org/10.1515/advgeom-2021-0037

Torelli S. On the Jacobian locus in the Prym locus and geodesics. Advances in Geometry. 2022 Jul 26;22(3):431-444. Epub 2021 Apr 18. doi: 10.1515/advgeom-2021-0037

Torelli, Sara. / On the Jacobian locus in the Prym locus and geodesics. In: Advances in Geometry. 2022 ; Vol. 22, No. 3. pp. 431-444.

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Research@Leibniz University