On the connectedness of the singular locus of the moduli space of principally polarized abelian varieties

Abstract

Let ${\mathcal{A}}_g$ denote the moduli space of principally polarized abelian varieties of dimension $g\ge 3.$ In this paper we prove the connectedness of the singular sublocus of ${\mathcal{A}}_g$ consisting of those abelian varieties which possess an involution different from $-id$.

arXiv comment15 pages. To appear in Moscow Mathematical Journal