103 citations · 107 across the 7 of their papers we have counts for
5 papers · 1 filter
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 .…
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…
When does the subadditivity theorem for multiplier ideals hold?
Shunsuke Takagi, Kei-ichi Watanabe
Demailly, Ein and Lazarsfeld \cite{DEL} proved the subadditivity theorem for multiplier ideals, which states the multiplier ideal of the product of ideals is contained in the produ…