For a Noetherian local domain $A$, there exists an upper bound $N_\tau(A)$ on the minimal number of
generators of any height two ideal $\mathfrak a$ for which $A/\mathfrak a$ is Cohen-Macaulay of type $\tau$. If $A$ contains an infinite field,
then we may take $N_\tau(A):=(\tau+1)e_{\textup{hom}}(A)$, where $e_{\textup{hom}}(A)$ is the homological multiplicity
of $A$.
Publié le : 2006-12-14
Classification:
number of generators,
Cohen-Macaulay ideals,
Noether Normalization,
homological multiplicity,
13E15,
3C14
@article{1168957347,
author = {Schoutens, Hans},
title = {Absolute bounds on the number of generators of Cohen-Macaulay ideals of height two},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {12},
number = {5},
year = {2006},
pages = { 719-732},
language = {en},
url = {http://dml.mathdoc.fr/item/1168957347}
}
Schoutens, Hans. Absolute bounds on the number of generators of Cohen-Macaulay ideals of height two. Bull. Belg. Math. Soc. Simon Stevin, Tome 12 (2006) no. 5, pp. 719-732. http://gdmltest.u-ga.fr/item/1168957347/