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 , the moduli space of complex principally polarized abelian varieties of dimension , and the maximal dimension of a compact subvariety through a very general point of . 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