6 citations · 9 across the 9 of their papers we have counts for
9 papers
On finite generating sets of infinitely generated ideals
Takafumi Shibuta
This paper presents a novel approach to constructing finite generating sets for infinitely generated ideals. By integrating algebraic and computational techniques, we provide a met…
An algorithm for computing the Hilbert--Samuel multiplicities and reductions of zero-dimensional ideals of Cohen--Macaulay local rings
Takafumi Shibuta, Shinichi Tajima
In this paper, we present an algorithm for computing the minimal reductions of -primary ideals of Cohen--Macaulay local rings. Using this algorithm, we are able to co…
Simple Polyominoes are Prime
Ayesha Asloob Qureshi, Takafumi Shibuta, Akihiro Shikama
In this paper we show that polyomino ideal of a simple polyomino coincides with the toric ideal of a weakly chordal bipartite graph and hence it has a quadratic Gröbner basis with…
Gröbner bases of contraction ideals
Takafumi Shibuta
We investigate Gröbner bases of contraction ideals under some monomial homomorphisms. As an application of our theorem, we generalize the result of Aoki--Hibi--Ohsugi--Takemura and…
Irreducibility criterion for algebroid curves
Takafumi Shibuta
The purpose of this paper is to give an algorithm for deciding the irreducibility of reduced algebroid curves over an algebraically closed field of arbitrary characteristic. To do…
One-dimensional rings of finite F-representation type
Takafumi Shibuta
We prove that a complete local or graded one-dimensional domain of prime characteristic has finite F-representation type if its residue field is algebraically closed or finite, and…
Toric ideals for high Veronese subrings of toric algebras
Takafumi Shibuta
We prove that the defining ideal of a sufficiently high Veronese subring of a toric algebra admits a quadratic Gröbner basis consisting of binomials. More generally, we prove that…
Log canonical thresholds of binomial ideals
Takafumi Shibuta, Shunsuke Takagi
We prove that the log canonical thresholds of a large class of binomial ideals, such as complete intersection binomial ideals and the defining ideals of space monomial curves, are…
Algorithms for computing multiplier ideals
Takafumi Shibuta
We give algorithms for computing multiplier ideals using Gröbner bases in Weyl algebras. The algorithms are based on a newly introduced notion which is a variant of Budur--Mustaţǎ-…