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arXiv · 2503.22305

Prym loci of branched double coverings and generalized Andreotti-Mayer loci

Atsushi Ikeda
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Abstract

The Andreotti-Mayer locus is a subset of the moduli space of principally polarized abelian varieties, defined by a condition on the dimension of the singular locus of the theta divisor. It is known that the Jacobian locus in the moduli space is an irreducible component of the Andreotti-Mayer locus. In this paper, we generalize the Andreotti-Mayer locus to the case of the moduli space of abelian varieties with non-principal polarization and prove that the Prym locus of branched double coverings is an irreducible component of the generalized Andreotti-Mayer locus.

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Atsushi Ikeda. 2025-11-15. Prym loci of branched double coverings and generalized Andreotti-Mayer loci. https://arxiv.org/abs/2503.22305

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