A generalization of tight closure and multiplier ideals
| dc.creator | Hara, Nobuo | |
| dc.creator | Yoshida, Ken-ichi | |
| dc.date | 2002-11-01 | |
| dc.date.accessioned | 2026-07-07T04:52:33Z | |
| dc.date.available | 2026-07-07T04:52:33Z | |
| dc.description | We introduce a new variant of tight closure associated to any fixed ideal $\a$, which we call $\a$-tight closure, and study various properties thereof. In our theory, the annihilator ideal $τ(\a)$ of all $\a$-tight closure relations, which is a generalization of the test ideal in the usual tight closure theory, plays a particularly important role. We prove the correspondence of the ideal $τ(\a)$ and the multiplier ideal associated to $\a$ (or, the adjoint of $\a$ in Lipman's sense) in normal $\Q$-Gorenstein rings reduced from characteristic zero to characteristic $p \gg 0$. Also, in fixed prime characteristic, we establish some properties of $τ(\a)$ similar to those of multiplier ideals (e.g., a Briançon-Skoda type theorem, subadditivity, etc.) with considerably simple proofs, and study the relationship between the ideal $τ(\a)$ and the F-rationality of Rees algebras. | |
| dc.description | about 35 pages, to appear in Trans. Amer. Math. Soc | |
| dc.identifier | https://arxiv.org/abs/math/0211008 | |
| dc.identifier | http://arxiv.org/abs/math/0211008 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65505 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 13A35;14B05 | |
| dc.title | A generalization of tight closure and multiplier ideals | |
| dc.type | text |