Pseudoreflections on Prym Varieties
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917386933764096 |
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| author | Auffarth, Robert Lahoz, Martí Naranjo, Juan Carlos |
| author_facet | Auffarth, Robert Lahoz, Martí Naranjo, Juan Carlos |
| contents | We show that for every g greater or equal than 5, the locus of Prym varieties in the moduli space of principally polarized abelian varieties of dimension g-1 that possess a pseudoreflection of geometric origin is the union of three different non-empty explicit irreducible families. This is in stark contrast to the loci of Jacobian varieties that possess a pseudoreflection of geometric origin, which is empty for any genus greater than 3. In g=6, a distinguished example of Prym varieties with a pseudoreflection is given by intermediate Jacobians of cubic threefolds that possess an Eckardt point. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_04940 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pseudoreflections on Prym Varieties Auffarth, Robert Lahoz, Martí Naranjo, Juan Carlos Algebraic Geometry 14L30, 14H40, 14K10 We show that for every g greater or equal than 5, the locus of Prym varieties in the moduli space of principally polarized abelian varieties of dimension g-1 that possess a pseudoreflection of geometric origin is the union of three different non-empty explicit irreducible families. This is in stark contrast to the loci of Jacobian varieties that possess a pseudoreflection of geometric origin, which is empty for any genus greater than 3. In g=6, a distinguished example of Prym varieties with a pseudoreflection is given by intermediate Jacobians of cubic threefolds that possess an Eckardt point. |
| title | Pseudoreflections on Prym Varieties |
| topic | Algebraic Geometry 14L30, 14H40, 14K10 |
| url | https://arxiv.org/abs/2412.04940 |