Shihoko Ishii, Ken-ichi Yoshida
Published 2024-10-20Version 1
We show the vanishing of the first direct image of the structure sheaf of a normal excellent scheme $X$ which is mapped properly and birationally over an excellent 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.
Comments: 10 pages, no figure
Vanishing of the higher direct images of the structure sheaf
Higher direct images of the structure sheaf in positive characteristic
Higher direct images of the structure sheaf via the Hilbert-Chow morphism
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