103 citations · 107 across the 7 of their papers we have counts for
8 papers
F-thresholds and Bernstein-Sato polynomials
Mircea Mustata, Shunsuke Takagi, Kei-ichi Watanabe
We introduce and study invariants of singularities in positive characteristic called F-thresholds. They give an analogue of the jumping coefficients of multiplier ideals in charact…
On F-pure thresholds
Shunsuke Takagi, Kei-ichi Watanabe
Using the Frobenius map, we introduce a new invariant for a pair $(R,\a)$ of a ring and an ideal $\a \subset R$, which we call the F-pure threshold $\mathrm{c}(\a)$ of $\a$, an…
Hilbert-Kunz multiplicity of three-dimensional local rings
Kei-ichi Watanabe, Ken-ichi Yoshida
In this paper, we investigate a lower bound (say ) on Hilbert-Kunz multiplicities for non-regular unmixed local rings of Krull dimension with characteristic .…
The total coordinate ring of a normal projective variety
E. Javier Elizondo, Kazuhiko Kurano, Kei-ichi Watanabe
The total coordinate ring TC(X) of a normal variety is a generalization of the ring introduced and studied by Cox in connection with a toric variety. Consider a normal projective v…
Minimal Hilbert-Kunz multiplicity
Kei-ichi Watanabe, Ken-ichi Yoshida
In this paper, we ask the following question: what is the minimal value of the difference for ideals with ? In order to answ…
Chains of integrally closed ideals
Kei-ichi Watanabe
Let be an excellent normal local ring with algebraically closed residue class field. Given integrally closed -primary ideals , we show that there…