A remark on the Castelnuovo-Mumford regularity of powers of ideal sheaves

Abstract

We show that a bound of the Castelnuovo-Mumford regularity of any power of the ideal sheaf of a smooth projective complex variety $X\subseteq {\mathbb{P}}^r$ is sharp exactly for complete intersections, provided the variety $X$ is cut out scheme-theoretically by several hypersurfaces in ${\mathbb{P}}^r$. This generalizes a result of Bertram-Ein-Lazarsfeld.

7 pages, to appear in the Journal of Pure and Applied Algebra