On Grauert-Riemenschneider vanishing for Cohen-Macaulay schemes of klt type
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915360076201984 |
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| author | Baudin, Jefferson Kawakami, Tatsuro Rösler, Linus |
| author_facet | Baudin, Jefferson Kawakami, Tatsuro Rösler, Linus |
| contents | Given a Cohen-Macaulay scheme of klt type $X$ and a resolution $π\colon Y\to X$, we show that $R^1π_*ω_Y=0$. We deduce that if $\mathrm{dim}(X)=3$, then $X$ satisfies Grauert-Riemenschneider vanishing and therefore has rational singularities. We also obtain that in arbitrary dimension, if $X$ is of finite type over a perfect field of characteristic $p>0$, then $X$ has $\mathbb{Q}_p$-rational singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_21381 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Grauert-Riemenschneider vanishing for Cohen-Macaulay schemes of klt type Baudin, Jefferson Kawakami, Tatsuro Rösler, Linus Algebraic Geometry 14F17, 14B05, 13A35 Given a Cohen-Macaulay scheme of klt type $X$ and a resolution $π\colon Y\to X$, we show that $R^1π_*ω_Y=0$. We deduce that if $\mathrm{dim}(X)=3$, then $X$ satisfies Grauert-Riemenschneider vanishing and therefore has rational singularities. We also obtain that in arbitrary dimension, if $X$ is of finite type over a perfect field of characteristic $p>0$, then $X$ has $\mathbb{Q}_p$-rational singularities. |
| title | On Grauert-Riemenschneider vanishing for Cohen-Macaulay schemes of klt type |
| topic | Algebraic Geometry 14F17, 14B05, 13A35 |
| url | https://arxiv.org/abs/2506.21381 |