2014/03/19 by Greco, Ornella, Martino, Ivan · 1 citation
#05E40 #13C14 #13D02 #13D40 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.1403.4796
We study the minimal free resolution of the Veronese modules of the polynomial ring in n variables, by giving a formula for the Betti numbers in terms of the reduced homology of some skeleton of a simplicial complex. We characterize when they are Cohen-Macaulay and we give a sufficient condition for the linearity of their minimal free resolution. We also conjecture that in 2 variables the Veronese modules have always pure resolutions. In addition, we give a closed formula for their Hilbert series. As an application of our results, we calculate the complete Betti diagrams of the Veronese subrings in three variables with degree 4 and 5, and in four variables with degree 3.