Caractères numériques

Abstract

The postulation of Arithmetically Cohen-Macaulay (ACM) subschemes of the projective space ${\mathbb P}^N_k$ 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 between these notions. The second, and most important aim, is to study the postulation of codimension 3 ACM subschemes of ${\mathbb P}^N$. We use a result of 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.