Veronese transform, and Castelnuovo-Mumford regularity of modules

Abstract

International audienceVeronese rings, Segre embeddings or more generally Segre-Veronese embeddings are very important rings in Algebraic Geometry. In this paper we present an original, elementary way to compute the Hilbert-Poincare series of these rings, as a consequence we compute their Castelnuovo-Mumford regularity, and also the leading term of the $h-$vector. Moreover, we can compute the Castelnuovo-Mumford regularity of the $n$-Veronese Module of any finitely generated Cohen-Macaulay graded module