F-thresholds, tight closure, integral closure, and multiplicity bounds
| dc.creator | Huneke, Craig | |
| dc.creator | Mustata, Mircea | |
| dc.creator | Takagi, Shunsuke | |
| dc.creator | Watanabe, Kei-ichi | |
| dc.date | 2007-08-17 | |
| dc.date | 2007-11-26 | |
| dc.date.accessioned | 2026-07-07T08:44:26Z | |
| dc.date.available | 2026-07-07T08:44:26Z | |
| dc.description | The F-threshold $c^J(\a)$ of an ideal $\a$ with respect to the ideal $J$ is a positive characteristic invariant obtained by comparing the powers of $\a$ with the Frobenius powers of $J$. We show that under mild assumptions, we can detect the containment in the integral closure or the tight closure of a parameter ideal using F-thresholds. We formulate a conjecture bounding $c^J(\a)$ in terms of the multiplicities $e(\a)$ and $e(J)$, when $\a$ and $J$ are zero-dimensional ideals, and $J$ is generated by a system of parameters. We prove the conjecture when $J$ is a monomial ideal in a polynomial ring, and also when $\a$ and $J$ are generated by homogeneous systems of parameters in a Cohen-Macaulay graded $k$-algebra. | |
| dc.description | 22 pages; v.2: minor changes, to appear in Michigan Math. J | |
| dc.identifier | https://arxiv.org/abs/0708.2394 | |
| dc.identifier | http://arxiv.org/abs/0708.2394 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142656 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 13A35 (Primary); 13B22, 13H15, 14B05 (Secondary) | |
| dc.title | F-thresholds, tight closure, integral closure, and multiplicity bounds | |
| dc.type | text |