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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2306.07830 |
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| _version_ | 1866915719364476928 |
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| author | Li, Sichen |
| author_facet | Li, Sichen |
| contents | In this paper, we first prove that every Mori dream surface $X$ satisfies the bounded cohomology property (BCP for short). Namely, there exists a constant $c_X>0$ such that $h^1(\mathcal O_X(C))\le c_Xh^0(\mathcal O_X(C))$ for every curve $C$ on $X$. We then prove that there is a positive constant $m(Y)$ such that $l_C:=(K_Y\cdot C)(C^2)^{-1}\le m(Y)$ for every ample curve $C$ on a geometrically ruled surface $Y$ over a curve of genus $g$, and $Y$ satisfies the BCP if $g\le1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_07830 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Smooth projective surfaces with bounded cohomology property Li, Sichen Algebraic Geometry In this paper, we first prove that every Mori dream surface $X$ satisfies the bounded cohomology property (BCP for short). Namely, there exists a constant $c_X>0$ such that $h^1(\mathcal O_X(C))\le c_Xh^0(\mathcal O_X(C))$ for every curve $C$ on $X$. We then prove that there is a positive constant $m(Y)$ such that $l_C:=(K_Y\cdot C)(C^2)^{-1}\le m(Y)$ for every ample curve $C$ on a geometrically ruled surface $Y$ over a curve of genus $g$, and $Y$ satisfies the BCP if $g\le1$. |
| title | Smooth projective surfaces with bounded cohomology property |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2306.07830 |