Secants to the Kummer Variety and the minimal Cohomological Class
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866911428854677504 |
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| author | Aburto, José Alejandro |
| author_facet | Aburto, José Alejandro |
| contents | We prove that, under certain conditions, the existence of a curve of $(m+2)$-secants to the Kummer variety of an indecomposable principally polarized abelian variety $X$, represents $m$-times the minimal cohomological class in $X$. In the case of $m=2$, we find an involution of such curve which proves that \(X\) is a Prym variety by results of Krichever-Grushevsky. This continues the work of Beauville and Debarre, who asked about the relation between some geometric properties of abelian varieties in a way to obtain a stratification of its moduli space. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2305_02943 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Secants to the Kummer Variety and the minimal Cohomological Class Aburto, José Alejandro Algebraic Geometry 14K25 (Primary) 14F05, 14H40 (Secondary) We prove that, under certain conditions, the existence of a curve of $(m+2)$-secants to the Kummer variety of an indecomposable principally polarized abelian variety $X$, represents $m$-times the minimal cohomological class in $X$. In the case of $m=2$, we find an involution of such curve which proves that \(X\) is a Prym variety by results of Krichever-Grushevsky. This continues the work of Beauville and Debarre, who asked about the relation between some geometric properties of abelian varieties in a way to obtain a stratification of its moduli space. |
| title | Secants to the Kummer Variety and the minimal Cohomological Class |
| topic | Algebraic Geometry 14K25 (Primary) 14F05, 14H40 (Secondary) |
| url | https://arxiv.org/abs/2305.02943 |