- Turkish Journal of Mathematics
- Vol: 40 Issue: 4
- Veronese transform and Castelnuovo-Mumford regularity of modules
Veronese transform and Castelnuovo-Mumford regularity of modules
Authors : Marcel Morales, Nguyen Thi Dung
Pages : 838-849
View : 7 | Download : 5
Publication Date : 9999-12-31
Article Type : Makaleler
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