Back to Search
Start Over
Multiplicity bounds in graded rings
- Source :
- Kyoto J. Math. 51, no. 1 (2011), 127-147
- Publication Year :
- 2009
-
Abstract
- The $F$-threshold $c^J(\a)$ of an ideal $\a$ with respect to an ideal $J$ is a positive characteristic invariant obtained by comparing the powers of $\a$ with the Frobenius powers of $J$. We study a conjecture formulated in an earlier paper \cite{HMTW} by the same authors together with M. Musta\c{t}\u{a}, which bounds $c^J(\a)$ 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 $\a$ and $J$ are generated by homogeneous systems of parameters in a Noetherian graded $k$-algebra. We also prove a similar inequality involving, instead of the $F$-threshold, the jumping number for the generalized parameter test submodules introduced in \cite{ST}.<br />Comment: 19 pages; v.2: a new section added, treating a comparison of F-thresholds and F-jumping numbers
Details
- Database :
- arXiv
- Journal :
- Kyoto J. Math. 51, no. 1 (2011), 127-147
- Publication Type :
- Report
- Accession number :
- edsarx.0912.3853
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1215/0023608X-2010-022