English

Compact Subvarieties of the Moduli Space of Complex Abelian Varieties

Algebraic Geometry 2025-11-24 v3 Number Theory

Abstract

We determine the maximal dimension of compact subvarieties of Ag\mathcal{A}_g, the moduli space of complex principally polarized abelian varieties of dimension gg, and the maximal dimension of a compact subvariety through a very general point of Ag\mathcal{A}_g. This also allows us to draw some conclusions for compact subvarieties of the moduli space of complex curves of compact type.

Keywords

Cite

@article{arxiv.2404.06009,
  title  = {Compact Subvarieties of the Moduli Space of Complex Abelian Varieties},
  author = {Samuel Grushevsky and Gabriele Mondello and Riccardo Salvati Manni and Jacob Tsimerman},
  journal= {arXiv preprint arXiv:2404.06009},
  year   = {2025}
}

Comments

v2: new version, expanded proofs and improved presentation. In particular, we added analysis of a missed case in the possible compact Shimura varieties to be considered. v3: revised version: exposition improved, results and proofs unchanged