Prym loci of branched double coverings and generalized Andreotti-Mayer loci
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917080438145024 |
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| author | Ikeda, Atsushi |
| author_facet | Ikeda, Atsushi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_22305 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Prym loci of branched double coverings and generalized Andreotti-Mayer loci Ikeda, Atsushi Algebraic Geometry 14H40, 14H42, 14K25 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. |
| title | Prym loci of branched double coverings and generalized Andreotti-Mayer loci |
| topic | Algebraic Geometry 14H40, 14H42, 14K25 |
| url | https://arxiv.org/abs/2503.22305 |