Ken-ichi Yoshida

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20242026

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math.AG2025

A variant of R{ö}hr's vanishing theorem with an application to the normal reduction number for normal surface singularities

Tomohiro Okuma, Kei-ichi Watanabe, Ken-ichi Yoshida

Let $A$ be an excellent two-dimensional normal local ring containing an algebraically closed field and let $X \to Spec (A)$ be a resolution of singularity. We prove a theor…

math.AG2025

Nearly Gorenstein rational surface singularities

Kyosuke Maeda, Tomohiro Okuma, Kei-ichi Watanabe +1

In this paper, we show that for any rational surface singularity $A$ , the canonical trace ideal $Tr_{A} (K_{A})$ is an integrally closed ideal, which is represented by the mini…

math.AG2024

On vanishing of higher direct images of the structure sheaf

Shihoko Ishii, Ken-ichi Yoshida

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 t…