Mathematics – Commutative Algebra
Scientific paper
2008-02-08
Mathematics
Commutative Algebra
Scientific paper
We show that bounds on the Castelnuovo-Mumford regularity of singular schemes, as a function of the degrees of the equations defining the shceme, of its dimension and of the dimension of their singular space. In the case where the singularities are isolated, we improve the bound given by Chardin and Ulrich, and in the general case we establish a bound doubly exponential in the dimension of the singular space. -- Nous montrons dans cet article des bornes pour la regularite de Castelnuovo-Mumford d'un schema admettant des singularites, en fonction des degres des equations definissant le schema, de sa dimension et de la dimension de son lieu singulier. Dans le cas ou les singularites sont isolees, nous ameliorons la borne fournie par Chardin et Ulrich et dans le cas general, nous etablissons une borne doublement exponentielle en la dimension du lieu singulier.
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