Compact Subvarieties of the Moduli Space of Complex Abelian Varieties

2024/04/09 by Grushevsky, Samuel, Mondello, Gabriele, Manni, Riccardo Salvati +1 · 2 citations
#14K10 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2404.06009

Abstract

We determine the maximal dimension of compact subvarieties of A_g, the moduli space of complex principally polarized abelian varieties of dimension g, and the maximal dimension of a compact subvariety through a very general point of A_g. This also allows us to draw some conclusions for compact subvarieties of the moduli space of complex curves of compact type.

Cited by

• Extremal effective curves and non-semiample line bundles on \rmM_g,n
• On the cohomological dimension of Siegel modular varieties and the modularity of formal Siegel modular forms

Related

• The Moduli Space of Abelian Varieties and the Singularities of the Theta Divisor
• Logarithmic abelian varieties, Part VII: Moduli
• Oort's conjecture for A_g
• Geometry of A_g and Its Compactifications
• Density and completeness of subvarieties of moduli spaces of curves or abelian varieties