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math.AC2003
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…
math.AC2002
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…
math.AC2002
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…