On a cohomological property of the center of a resolution
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866914619767914496 |
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| author | Kim, Donghyeon |
| author_facet | Kim, Donghyeon |
| contents | In this note, we explore the cohomological property of the codimension of the center of a resolution. In particular, we define a resolution $f:X'\to X$ to be $q$-birational if the center of $f$ satisfies $\mathrm{codim} \,\mathrm{Cent}(f)\ge q+1$, and we prove that $R^if_*\mathcal{O}_X(E)=0$ for every $1\le i\le q-1$ and every $f$-anti-nef effective $f$-exceptional divisor $E$ on $X'$ if $X$ is $(R_q)$ and $(S_{q+1})$. We also discuss a partial converse of the theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_07720 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On a cohomological property of the center of a resolution Kim, Donghyeon Algebraic Geometry 14B05, 14E05 In this note, we explore the cohomological property of the codimension of the center of a resolution. In particular, we define a resolution $f:X'\to X$ to be $q$-birational if the center of $f$ satisfies $\mathrm{codim} \,\mathrm{Cent}(f)\ge q+1$, and we prove that $R^if_*\mathcal{O}_X(E)=0$ for every $1\le i\le q-1$ and every $f$-anti-nef effective $f$-exceptional divisor $E$ on $X'$ if $X$ is $(R_q)$ and $(S_{q+1})$. We also discuss a partial converse of the theorem. |
| title | On a cohomological property of the center of a resolution |
| topic | Algebraic Geometry 14B05, 14E05 |
| url | https://arxiv.org/abs/2209.07720 |