Frobenius liftable hypersurfaces
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911060537114624 |
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| author | Kawakami, Tatsuro Sarkar, Supravat Witaszek, Jakub |
| author_facet | Kawakami, Tatsuro Sarkar, Supravat Witaszek, Jakub |
| contents | Let $D$ be a reduced divisor in $\mathbb P^n_k$ for an algebraically closed field $k$ of positive characteristic $p > 0$. We prove that if $(\mathbb P^n_k, D)$ is Frobenius liftable modulo $p^2$, then $D$ is a toric divisor. As a corollary, we show that if there exists a finite surjective morphism $f\colon Y\to X$ onto a smooth projective complex variety $X$ of Picard rank $1$ such that $(Y, f^{-1}(D)_{\mathrm{red}})$ is a toric pair, then $X$ is the projective space and $D$ is a toric divisor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_12198 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Frobenius liftable hypersurfaces Kawakami, Tatsuro Sarkar, Supravat Witaszek, Jakub Algebraic Geometry 13A35, 14M25 Let $D$ be a reduced divisor in $\mathbb P^n_k$ for an algebraically closed field $k$ of positive characteristic $p > 0$. We prove that if $(\mathbb P^n_k, D)$ is Frobenius liftable modulo $p^2$, then $D$ is a toric divisor. As a corollary, we show that if there exists a finite surjective morphism $f\colon Y\to X$ onto a smooth projective complex variety $X$ of Picard rank $1$ such that $(Y, f^{-1}(D)_{\mathrm{red}})$ is a toric pair, then $X$ is the projective space and $D$ is a toric divisor. |
| title | Frobenius liftable hypersurfaces |
| topic | Algebraic Geometry 13A35, 14M25 |
| url | https://arxiv.org/abs/2507.12198 |