Tomohiro Okuma

activity

20242026

collaborators

6 papers

math.AC2026

Nearly Gorenstein normal graded rings

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

We investigate nearly Gorenstein property for a normal graded ring $R = ⨁_{n \geq 0} R_{n}$ finitely generated over a field. For that purpose, we investigate $K_{R}^{- 1}$ , the i…

math.AC2026

On Gorensteinness of associated graded rings of filtrations

Meghana Bhat, Saipriya Dubey, Shreedevi K. Masuti +4

Let $(A, m)$ be a Gorenstein local ring, and $F = {F_{n}}_{n \in Z}$ a Hilbert filtration. In this paper, we give a criterion for Gorensteinness of the…

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.AG2025

A variant of R{Ã¶}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.AC2025

Gorenstein Normal tangent cones of integrally closed ideals in two-dimensional normal singularities

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

Let $(A, m)$ be a two-dimensional excellent normal Gorenstein local domain containing an algebraically closed filed. Let $I = H^{0} (X, O_{X} (- Z)) \subset A$ be an $\ma…

math.AC2024

A Geometric description of almost Gorensteinness for two-dimensional normal singularities

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

Let $A$ be an excellent two-dimensional normal local ring containing an algebraically closed field. Then $A$ is called an elliptic singularity if $p_{f} (A) = 1$ , where $p_{f}$ denotes th…