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6 papers · 1 filter
Multigraded rings, diagonal subalgebras, and rational singularities
Kazuhiko Kurano, Ei-ichi Sato, Anurag K. Singh +1
We study the properties of F-rationality and F-regularity in multigraded rings and their diagonal subalgebras. The main focus is on diagonal subalgebras of bigraded rings: these co…
F-thresholds, tight closure, integral closure, and multiplicity bounds
Craig Huneke, Mircea Mustata, Shunsuke Takagi +1
The F-threshold $c^J(\a)$ of an ideal $\a$ with respect to the ideal is a positive characteristic invariant obtained by comparing the powers of $\a$ with the Frobenius powers o…
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…
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…