Length, multiplicity, and multiplier ideals
| dc.creator | de Fernex, Tommaso | |
| dc.date | 2004-09-26 | |
| dc.date.accessioned | 2026-07-07T05:12:35Z | |
| dc.date.available | 2026-07-07T05:12:35Z | |
| dc.description | Let (R,m) be an n-dimensional regular local ring, essentially of finite type over a field of characteristic zero. In this paper we study the relationship between the singularities of the scheme defined by an m-primary ideal I of R and the multiplier ideals J(I^c), with c varying among the positive rational numbers. In particular, we prove that, for every nonnegative integer k, the Samuel multiplicity of I is greater or equal to (n+k)^n/c^n whenever J(I^c) is contained in the (k+1)-th power of the maximal ideal m. This formula generalizes an inequality on log canonical thresholds previously obtained by Ein, Mustaţǎ and the author of this paper (arXiv:math.AG/0205171). A refined inequality is also shown to hold for small dimensions, and similar results valid for a generalization of test ideals in positive characteristics are presented. | |
| dc.description | 15 pages; to appear in Trans. Amer. Math. Soc | |
| dc.identifier | https://arxiv.org/abs/math/0409500 | |
| dc.identifier | http://arxiv.org/abs/math/0409500 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72629 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Commutative Algebra | |
| dc.subject | 14B05 (primary); 13H05, 14B07, 13H15 (secondary) | |
| dc.title | Length, multiplicity, and multiplier ideals | |
| dc.type | text |