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

Sebastián Reyes-Carocca, Rubí E. Rodríguez

Departamento de Matemática y Estadística, Universidad de La Frontera, Avenida Francisco Salazar 01145, Casilla 54-D, Temuco, Chile

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 $-\mathrm{id}$.

Key words and phrases: Abelian varieties, Jacobian varieties, Group actions.

MSC: 14K10, 14L30

Language: English

DOI: 10.17323/1609-4514-2018-18-3-473-489

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