On the Euler characteristic of weakly ordinary varieties of maximal Albanese dimension
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912461232275456 |
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| author | Baudin, Jefferson |
| author_facet | Baudin, Jefferson |
| contents | We show that a smooth proper weakly ordinary variety $X$ of maximal Albanese dimension satisfies $χ(X, ω_X) \geq 0$. We also show that if $X$ is not of general type, then $χ(X, ω_X) = 0$ and the Albanese image of $X$ is fibered by abelian varieties. The proof uses the positive characteristic generic vanishing theory developed by Hacon-Patakfalvi, as well as our recent Witt vector version of Grauert-Riemenschneider vanishing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01797 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Euler characteristic of weakly ordinary varieties of maximal Albanese dimension Baudin, Jefferson Algebraic Geometry 14K05, 14G17, 14F17 We show that a smooth proper weakly ordinary variety $X$ of maximal Albanese dimension satisfies $χ(X, ω_X) \geq 0$. We also show that if $X$ is not of general type, then $χ(X, ω_X) = 0$ and the Albanese image of $X$ is fibered by abelian varieties. The proof uses the positive characteristic generic vanishing theory developed by Hacon-Patakfalvi, as well as our recent Witt vector version of Grauert-Riemenschneider vanishing. |
| title | On the Euler characteristic of weakly ordinary varieties of maximal Albanese dimension |
| topic | Algebraic Geometry 14K05, 14G17, 14F17 |
| url | https://arxiv.org/abs/2507.01797 |