Jets-separation thresholds, Seshadri constants and higher Gauss-Wahl maps on abelian varieties
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915278796881920 |
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| author | Alvarado, Nelson |
| author_facet | Alvarado, Nelson |
| contents | Given a closed subscheme $Z$ of a polarized abelian variety $(A,\ell)$ we define its vanishing threshold with respect to $\ell$ and relate it to the Seshadri constant of the ideal defining $Z.$ As a particular case, we introduce the notion of jets-separation thresholds, which naturally arise as the vanishing threshold of the $p$-infinitesimal neighborhood of a point. Afterwards, by means of Fourier-Mukai methods we relate the jets-separation thresholds with the surjectivity of certain higher Gauss-Wahl maps. As a consequence we obtain a criterion for the surjectivity of those maps in terms of the Seshadri constant of the polarization $\ell.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20769 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Jets-separation thresholds, Seshadri constants and higher Gauss-Wahl maps on abelian varieties Alvarado, Nelson Algebraic Geometry Given a closed subscheme $Z$ of a polarized abelian variety $(A,\ell)$ we define its vanishing threshold with respect to $\ell$ and relate it to the Seshadri constant of the ideal defining $Z.$ As a particular case, we introduce the notion of jets-separation thresholds, which naturally arise as the vanishing threshold of the $p$-infinitesimal neighborhood of a point. Afterwards, by means of Fourier-Mukai methods we relate the jets-separation thresholds with the surjectivity of certain higher Gauss-Wahl maps. As a consequence we obtain a criterion for the surjectivity of those maps in terms of the Seshadri constant of the polarization $\ell.$ |
| title | Jets-separation thresholds, Seshadri constants and higher Gauss-Wahl maps on abelian varieties |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2407.20769 |