Secant loci on moduli of Prym varieties
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
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| _version_ | 1866918151609909248 |
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| author | Farkas, Gavril Lelli-Chiesa, Margherita |
| author_facet | Farkas, Gavril Lelli-Chiesa, Margherita |
| contents | We present a Prym analogue of Lazarsfeld's result that curves on general polarized K3 surfaces verify the Brill-Noether Theorem, or equivalently, that their canonical embedding has no unexpected secants. We show that the Prym-canonical embedding of a curve on a general Nikulin surface (both of standard and non-standard types) has no unexpected secants. We then explain how these geometric facts suffice to determine the class of the universal difference divisor on the moduli space of stable Prym curves of (odd) genus g. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_26118 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Secant loci on moduli of Prym varieties Farkas, Gavril Lelli-Chiesa, Margherita Algebraic Geometry We present a Prym analogue of Lazarsfeld's result that curves on general polarized K3 surfaces verify the Brill-Noether Theorem, or equivalently, that their canonical embedding has no unexpected secants. We show that the Prym-canonical embedding of a curve on a general Nikulin surface (both of standard and non-standard types) has no unexpected secants. We then explain how these geometric facts suffice to determine the class of the universal difference divisor on the moduli space of stable Prym curves of (odd) genus g. |
| title | Secant loci on moduli of Prym varieties |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2509.26118 |