Caractères numériques

Details Caractères numériques Caractères numériques

2004-01-27

arxiv.org/abs/math/0401375v1

Mathematics

Algebraic Geometry

25 pages latex

Scientific paper

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.

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