The postulation of Aritméticamente Cohen-Macaulay (ACM) subschemes of the projective space PkN is well known in the case of codimension 2. There are many different ways of recording this numerical information: numerical character of Gruson/Peskine, h-vector, postulation character of Martin-Deschamps/Perrin... The first aim of this paper is to show the equivalence of these notions. The second and most important aim, is to study the postulation of codimension 3 ACM subschemes of PN. We use a result by Macaulay which describes all the Hilbert functions of the quotients of a polynomial ring. By iterating the number of variables, we obtain a new form of the growth of these functions.
@article{urn:eudml:doc:44347,
title = {Caract\`eres num\'eriques et fonctions de Macaulay.},
journal = {Collectanea Mathematica},
volume = {55},
year = {2004},
pages = {289-314},
zbl = {1065.14061},
mrnumber = {MR2099220},
language = {fr},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44347}
}
Martin-Deschamps, Mireille. Caractères numériques et fonctions de Macaulay.. Collectanea Mathematica, Tome 55 (2004) pp. 289-314. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44347/