Tomohiro Okuma

activity

20052026

most citedThe geometric genus of splice-quotient singularities

63 citations · 237 across the 22 of their papers we have counts for

collaborators

23 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.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.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…

math.AC2024

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.AG2024

The multiplicity of cyclic coverings of a singularity of an algebraic variety

Toya Kumagai, Tomohiro Okuma

Let $V$ be an affine algebraic variety, and let $p \in V$ be a singular point. For a regular function $g$ on $V$ such that $g (p) = 0$ and for a positive integer $n$ , we consider the c…

math.AC2023★ 1 cited

Gorensteinness for normal tangent cones of elliptic ideals

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

Let $A$ be a two-dimensional excellent normal Gorenstein local domain. In this paper, we characterize elliptic ideals $I \subset A$ for its normal tangent cone $G (I)$ to…

math.AC2020★ 10 cited

Normal Hilbert coefficients and elliptic ideals in normal two-dimensional singularities

Tomohiro Okuma, Maria Evelina Rossi, Kei-ichi Watanabe +1

Let $(A, m)$ be an excellent two-dimensional normal local domain. In this paper we study the elliptic and the strongly elliptic ideals of $A$ with the aim to characterize…

math.AG2020

Weighted homogeneous surface singularities homeomorphic to Brieskorn complete intersections

Tomohiro Okuma

For a given topological type of a normal surface singularity, there are various types of complex structures which realize it. We are interested in the following problem: Find the m…

math.AG2019

Normal reduction numbers of normal surface singularities

Tomohiro Okuma

This article consists of two parts. The first part is a survey on the normal reduction numbers of normal surface singularities. It includes results on elliptic singularities, cone-…

math.AC2019★ 2 cited

The normal reduction number of two-dimensional cone-like singularities

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

Let $(A, m)$ be a normal two-dimensional local ring and $I$ an $m$ -primary integrally closed ideal with a minimal reduction $Q$ . Then we calculate the numbers:…

math.AC2018★ 12 cited

Normal reduction numbers for normal surface singularities with application to elliptic singularities of Brieskorn type

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

In this paper, we give a formula for normal reduction number of an integrally closed $m$ -primary ideal of a $2$ -dimensional normal local ring $(A, m)$ in terms o…

math.AG2018★ 7 cited

Cohomology of ideals in elliptic surface singularities

Tomohiro Okuma

We introduce the the normal reduction number of two-dimensional normal singularities and prove that elliptic singularity has normal reduction number two. We also prove that for a t…

math.AG2017★ 9 cited

Analytic singularities supported by a specific integral homology sphere link

András Némethi, Tomohiro Okuma

The main question we target is the following: If one fixes a topological type of a complex normal surface singularity then what are the possible analytic types supported by it, and…

math.AC2015★ 25 cited

Rees algebras and $p_{g}$ -ideals in a two-dimensional normal local domain

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

The authors introduced the notion of $p_{g}$ -ideals for two-dimensional excellent normal local domain over an algebraicaly closed field in terms of resolution of singularities. In th…

math.AG2015★ 18 cited

A characterization of two-dimensional rational singularities via Core of ideals

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

The notion of $p_{g}$ -ideals for normal surface singularities has been proved to be very useful. On the other hand, the core of ideals has been proved to be very important concept an…

math.AC2014★ 20 cited

Good ideals and $p_{g}$ -ideals in two-dimensional normal singularities

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

In this paper, we introduce the notion of $p_{g}$ -ideals and $p_{g}$ -cycles, which inherits nice properties of integrally closed ideals on rational singularities. As an application, we…

math.AG2010★ 3 cited

The multiplicity of abelian covers of splice quotient singularities

Tomohiro Okuma

From a resolution graph with certain conditions, Neumann and Wahl constructed an equisingular family of surface singularities called splice quotients. For this class some fundament…

math.AG2009★ 5 cited

The embedding dimension of weighted homogeneous surface singularities

András Némethi, Tomohiro Okuma

We analyze the embedding dimension of a normal weighted homogeneous surface singularity, and more generally, the Poincaré series of the minimal set of generators of the graded alge…

math.AG2006★ 46 cited

On the Casson Invariant Conjecture of Neumann--Wahl

Andras Nemethi, Tomohiro Okuma

In the article we prove the Casson Invariant Conjecture of Neumann--Wahl for splice type surface singularities. Namely, for such an isolated complete intersection, whose link is an…

math.AG2006★ 63 cited

The geometric genus of splice-quotient singularities

Tomohiro Okuma

We prove a formula for the geometric genus of splice-quotient singularities (in the sense of Neumann and Wahl). This formula enables us to compute the invariant from the resolution…

math.AG2005★ 16 cited

Universal abelian covers of certain surface singularities

Tomohiro Okuma

Every normal complex surface singularity with $Q$ -homology sphere link has a universal abelian cover. It has been conjectured by Neumann and Wahl that the universal abelian…

Nearly Gorenstein normal graded rings

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

Nearly Gorenstein rational surface singularities

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

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

On Gorensteinness of associated graded rings of filtrations

The multiplicity of cyclic coverings of a singularity of an algebraic variety

Gorensteinness for normal tangent cones of elliptic ideals

Normal Hilbert coefficients and elliptic ideals in normal two-dimensional singularities

Weighted homogeneous surface singularities homeomorphic to Brieskorn complete intersections

Normal reduction numbers of normal surface singularities

The normal reduction number of two-dimensional cone-like singularities

Normal reduction numbers for normal surface singularities with application to elliptic singularities of Brieskorn type

Cohomology of ideals in elliptic surface singularities

Analytic singularities supported by a specific integral homology sphere link

Rees algebras and pg​-ideals in a two-dimensional normal local domain

A characterization of two-dimensional rational singularities via Core of ideals

Good ideals and pg​-ideals in two-dimensional normal singularities

The multiplicity of abelian covers of splice quotient singularities

The embedding dimension of weighted homogeneous surface singularities

On the Casson Invariant Conjecture of Neumann--Wahl

The geometric genus of splice-quotient singularities

Universal abelian covers of certain surface singularities

Rees algebras and $p_{g}$ -ideals in a two-dimensional normal local domain

Good ideals and $p_{g}$ -ideals in two-dimensional normal singularities