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Article Dans Une Revue Quarterly Journal of Mathematics Année : 2022

Real moduli spaces and density of non-simple real abelian varieties

Résumé

Abstract For fixed k < g and a family of polarized abelian varieties of dimension g over ${{\mathbb{R}}}$, we give a criterion for the density in the parameter space of those abelian varieties over ${{\mathbb{R}}}$ containing a k-dimensional abelian subvariety over ${{\mathbb{R}}}$. As application, we prove density of such a set in the moduli space of polarized real abelian varieties of dimension g and density of real algebraic curves mapping non-trivially to real k-dimensional abelian varieties in the moduli space of real algebraic curves as well as in the space of real plane curves. This extends to the real setting results by Colombo and Pirola [10]. We then consider the real locus of an algebraic stack over $\mathbb{R}$, attaching a topological space to it. For a real moduli stack, this defines a real moduli space. We show that for ${{\mathcal{M}}}_g$ and ${{\mathcal{A}}}_g$, the real moduli spaces that arise in this way coincide with the moduli spaces of Gross–Harris [13] and Seppälä–Silhol [23].

Dates et versions

hal-04003077 , version 1 (23-02-2023)

Identifiants

Citer

Olivier de Gaay Fortman. Real moduli spaces and density of non-simple real abelian varieties. Quarterly Journal of Mathematics, 2022, 73 (3), pp.969-989. ⟨10.1093/qmath/haab060⟩. ⟨hal-04003077⟩
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