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Birational invariance of \(H^1({\mathcal {O}})\)

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Abstract

We show a vanishing result for the first direct image of a proper birational morphism of normal quasi-excellent schemes with regular codomain. As a consequence, we deduce the birational invariance of \(H^1(X,{\mathcal {O}}_X)\) for regular quasi-excellent schemes X. More generally, this is shown for quasi-excellent X which are \(S_3\) and pseudo-rational in codimension 2.

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I am grateful to the referee for helpful comments.

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  1. Springer-Verlag, Tiergartenstr. 17, 69121, Heidelberg, Germany

    Rémi Lodh

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  1. Rémi Lodh
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Lodh, R. Birational invariance of \(H^1({\mathcal {O}})\). Arch. Math. 122, 163–170 (2024). https://doi.org/10.1007/s00013-023-01939-x

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