Characterizations of freeness for Cohen-Macaulay spaces

Delphine Pol (1)

1 LAREMA - Laboratoire Angevin de Recherche en Mathématiques

The purpose of this paper is to develop an analogue of freeness for reduced Cohen-Macaulay spaces embedded in a smooth manifold S which generalizes the notion of Saito free divisors. The main result of this paper is a characterization of freeness in terms of the projective dimension of the module of multi-logarithmic k-forms, where k is the codimension of X in S. We then focus on quasi-homogeneous complete intersection curves, for which we compute explicitly a minimal free resolution of the module of multi-residues and the module of multi-logarithmic forms.

Mots clés: logarithmic differential forms; logarithmic residues; complete intersections; curves; Cohen-Macaulay

Domaines: Géométrie algébrique [math.AG]

Delphine Pol. Characterizations of freeness for Cohen-Macaulay spaces. 2015. ⟨hal-01248123v2⟩