Totally geodesic subvarieties in the moduli space of curves

Alessandro Ghigi; Gian Pietro Pirola; Sara Torelli

Totally geodesic subvarieties in the moduli space of curves

Algebraic Geometry 2019-02-19 v1

Authors: Alessandro Ghigi , Gian Pietro Pirola , Sara Torelli

Abstract

In this paper we study totally geodesic subvarieties $Y \subset \mathsf{A}_g$ of the moduli space of principally polarized abelian varieties with respect to the Siegel metric, for $g\geq 4$ . We prove that if $Y$ is generically contained in the Torelli locus, then $\dim Y \leq (7g -2)/3$ .

Keywords

totally geodesic subvarieties moduli space of curves principally polarized abelian varieties siegel metric torelli locus

Cite

@article{arxiv.1902.06098,
  title  = {Totally geodesic subvarieties in the moduli space of curves},
  author = {Alessandro Ghigi and Gian Pietro Pirola and Sara Torelli},
  journal= {arXiv preprint arXiv:1902.06098},
  year   = {2019}
}

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