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arXiv · 2410.15282

On vanishing of higher direct images of the structure sheaf

Shihoko Ishii·Ken-ichi Yoshida
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Abstract

We show the vanishing of the first direct image of the structure sheaf of a normal scheme $X$ which is mapped properly and birationally over a regular scheme of any dimension. On the other hand, for any dimension greater than two, we show examples of a proper birational morphism from a normal and Cohen-Macaulay scheme to a regular scheme such that the second direct image does not vanish and has an isolated support.

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Shihoko Ishii, Ken-ichi Yoshida. 2024-10-20. On vanishing of higher direct images of the structure sheaf. https://arxiv.org/abs/2410.15282

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