103 citations · 103 across the 5 of their papers we have counts for
6 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…
Formulas for multiplier ideals on singular varieties
Shunsuke Takagi
We prove a generalization of Demailly-Ein-Lazarsfeld's subadditivity formula and Mustata's summation formula for multiplier ideals to the case of singular varieties, using characte…
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…
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…
On a generalization of test ideals
Nobuo Hara, Shunsuke Takagi
The test ideal of a ring of prime characteristic is an important object in the theory of tight closure. In this paper, we study a generalization of the test ideal, which…
An interpretation of multiplier ideals via tight closure
Shunsuke Takagi
Hara and Smith independently proved that in a normal $\mQ$-Gorenstein ring of characteristic , the test ideal coincides with the multiplier ideal associated to the trivial…