Veronese transform and Castelnuovo Mumford regularity of modules

Abstract

: Veronese 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 Poincar´e series of these rings; as a consequence we compute their Castelnuovo Mumford regularity and also the highest graded Betti number. Moreover, using the Castelnuovo Mumford regularity of a Cohen Macaulay finitely generated graded module, we compute that of its Veronese transforms.