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arXiv · 2506.21381

On Grauert-Riemenschneider vanishing for Cohen-Macaulay schemes of klt type

Jefferson Baudin·Tatsuro Kawakami·Linus Rösler
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Abstract

Given a Cohen-Macaulay scheme of klt type $X$ and a resolution $\pi\colon Y\to X$, we show that $R^1\pi_*\omega_Y=0$. 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.

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Jefferson Baudin, Tatsuro Kawakami, Linus Rösler. 2025-06-26. On Grauert-Riemenschneider vanishing for Cohen-Macaulay schemes of klt type. https://arxiv.org/abs/2506.21381

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