Veronese transform and Castelnuovo-Mumford regularity of modules

Authors : Marcel MORALES, Nguyen Thi DUNG

Pages : 838-849

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Publication Date : 0000-00-00

Article Type : Research Paper

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.
Keywords : Castelnuovo Mumford regularity, Veronese ring, Segre ring, Hilbert Series