On the Jacobian locus in the Prym locus and geodesics

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

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  • Sara Torelli

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OriginalspracheEnglisch
Seiten (von - bis)431-444
Seitenumfang14
FachzeitschriftAdvances in Geometry
Jahrgang22
Ausgabenummer3
Frühes Online-Datum18 Apr. 2021
PublikationsstatusVeröffentlicht - 26 Juli 2022

Abstract

In the paper we consider the Jacobian locus \(\overline{J_g}\) and the Prym locus \(\overline{P_{g+1}}\), in the moduli space \(A_g\) of principally polarized abelian varieties of dimension \(g\), for \(g\geq 7\), and we study the extrinsic geometry of \(\overline{J_g}\subset \overline{P_{g+1}}\), 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 \(A_g\), starting at a Jacobian variety \([JC]\in A_g\) of a curve \([C]\in M_g\) and with direction \(\zeta\in T_{[JC]}J_g\). We prove that for a general \(JC\), any geodesic of this kind is not contained in \(\overline{J_g}\) and even in \(\overline{P_{g+1}}\), if \(\zeta\) has rank $k

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On the Jacobian locus in the Prym locus and geodesics. / Torelli, Sara.
in: Advances in Geometry, Jahrgang 22, Nr. 3, 26.07.2022, S. 431-444.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

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 ; Jahrgang 22, Nr. 3. S. 431-444.
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