Syzygies of the Veronese Modules

@article{Greco2014SyzygiesOT,
title={Syzygies of the Veronese Modules},
author={O. Greco and I. Martino},
journal={Communications in Algebra},
year={2014},
volume={44},
pages={3890 - 3906}
}
• Published 2014
• Mathematics
• Communications in Algebra
• We study the minimal free resolution of the Veronese modules, Sn, d, k = ⊕i≥0Sk+id, where S = 𝕂[x1,…, xn], by giving a formula for the Betti numbers in terms of the reduced homology of some skeleton of a simplicial complex. We prove that Sn, d, k is Cohen–Macaulay if and only if k < d, and that its minimal resolution is pure and has some linearity features when k > d(n − 1) − n. We prove combinatorially that the resolution of S2, d, k is pure. We show that . As an application, we calculate the… CONTINUE READING
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