Veronese transform, and Castelnuovo-Mumford regularity of modules

Marcel Morales (1) , Dung Nguyen Thi (2)

1 IF - Institut Fourier
2 Thai Nguyen University of Agriculture and Foresty

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-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.

Mots clés: Veronese ring; Segre ring; Castelnuovo-Mumford regularity; Hilbert Series

Domaines: Algèbre commutative [math.AC]

Marcel Morales, Dung Nguyen Thi. Veronese transform, and Castelnuovo-Mumford regularity of modules. Turkish Journal of Mathematics, 2016, 40 (4), pp.838-849. ⟨hal-00963895⟩