Turkish Journal of Mathematics
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.
DOI
10.3906/mat-1411-45
Keywords
Castelnuovo-Mumford regularity, Veronese ring, Segre ring, Hilbert Series
First Page
838
Last Page
849
Recommended Citation
MORALES, M, & DUNG, N. T (2016). Veronese transform and Castelnuovo-Mumford regularity of modules. Turkish Journal of Mathematics 40 (4): 838-849. https://doi.org/10.3906/mat-1411-45
