Analysis reveals Grauert-Riemenschneider vanishing in Cohen-Macaulay schemes, suggesting rational singularities.
Given a Cohen-Macaulay scheme of klt type X and a resolution π Y→ X, we show that R¹π_*ωY=0. We deduce that if 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 Qₚ-rational singularities.
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Baudin et al. (2025) studied this question.
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