samuel multiplicity
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2019 ◽  
Vol 30 (02) ◽  
pp. 379-396
Author(s):  
V. H. Jorge Pérez ◽  
T. H. Freitas

Let [Formula: see text] be a commutative quasi-local ring (with identity [Formula: see text]), and let [Formula: see text] be an [Formula: see text]-ideal such that [Formula: see text]. For [Formula: see text] an Artinian [Formula: see text]-module of N-dimension [Formula: see text], we introduce the notion of Hilbert-coefficients of [Formula: see text] relative to [Formula: see text] and give several properties. When [Formula: see text] is a co-Cohen–Macaulay [Formula: see text]-module, we establish the Northcott’s inequality for Artinian modules. As applications, we show some formulas involving the Hilbert coefficients and we investigate the behavior of these multiplicities when the module is the local cohomology module.



2015 ◽  
Vol 91 (2) ◽  
pp. 191-201 ◽  
Author(s):  
CARLES BIVIÀ-AUSINA

AbstractWe obtain a characterisation of the monomial ideals $I\subseteq \mathbb{C}[x_{1},\dots ,x_{n}]$ of finite colength that satisfy the condition $e(I)={\mathcal{L}}_{0}^{(1)}(I)\cdots {\mathcal{L}}_{0}^{(n)}(I)$, where ${\mathcal{L}}_{0}^{(1)}(I),\dots ,{\mathcal{L}}_{0}^{(n)}(I)$ is the sequence of mixed Łojasiewicz exponents of $I$ and $e(I)$ is the Samuel multiplicity of $I$. These are the monomial ideals whose integral closure admits a reduction generated by homogeneous polynomials.



2013 ◽  
Vol 212 ◽  
pp. 59-85 ◽  
Author(s):  
Ian M. Aberbach ◽  
Florian Enescu

AbstractWe present results on the Watanabe–Yoshida conjecture for the Hilbert–Kunz multiplicity of a local ring of positive characteristic. By improving on a “volume estimate” giving a lower bound for Hilbert–Kunz multiplicity, we obtain the conjecture when the ring has either Hilbert–Samuel multiplicity less than or equal to 5 or dimension less than or equal to 6. For nonregular rings with fixed dimension, a new lower bound for the Hilbert–Kunz multiplicity is obtained.



2013 ◽  
Vol 212 ◽  
pp. 59-85
Author(s):  
Ian M. Aberbach ◽  
Florian Enescu

AbstractWe present results on the Watanabe–Yoshida conjecture for the Hilbert–Kunz multiplicity of a local ring of positive characteristic. By improving on a “volume estimate” giving a lower bound for Hilbert–Kunz multiplicity, we obtain the conjecture when the ring has either Hilbert–Samuel multiplicity less than or equal to 5 or dimension less than or equal to 6. For nonregular rings with fixed dimension, a new lower bound for the Hilbert–Kunz multiplicity is obtained.



2013 ◽  
Vol 62 (10) ◽  
pp. 1361-1364
Author(s):  
Tao Yu


2012 ◽  
Vol 56 (6) ◽  
pp. 1213-1231 ◽  
Author(s):  
QingPing Zeng ◽  
HuaiJie Zhong ◽  
ZhenYing Wu


2012 ◽  
Vol 23 (06) ◽  
pp. 1250065 ◽  
Author(s):  
JÓN I. MAGNÚSSON ◽  
ALEXANDER RASHKOVSKII ◽  
RAGNAR SIGURDSSON ◽  
PASCAL J. THOMAS

Let Ω be a bounded hyperconvex domain in ℂn, 0 ∈ Ω, and Sε a family of N poles in Ω, all tending to 0 as ε tends to 0. To each Sε we associate its vanishing ideal [Formula: see text] and pluricomplex Green function [Formula: see text]. Suppose that, as ε tends to 0, [Formula: see text] converges to [Formula: see text] (local uniform convergence), and that (Gε)ε converges to G, locally uniformly away from 0; then [Formula: see text]. If the Hilbert–Samuel multiplicity of [Formula: see text] is strictly larger than its length (codimension, equal to N here), then (Gε)ε cannot converge to [Formula: see text]. Conversely, if [Formula: see text] is a complete intersection ideal, then (Gε)ε converges to [Formula: see text]. We work out the case of three poles.



2007 ◽  
Vol 339 (1) ◽  
pp. 21-35 ◽  
Author(s):  
Jörg Eschmeier


2007 ◽  
Vol 56 (3) ◽  
pp. 1463-1478 ◽  
Author(s):  
Joerg Eschmeier
Keyword(s):  


2004 ◽  
Vol 186 (2) ◽  
pp. 411-437 ◽  
Author(s):  
Xiang Fang


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