Greco, Ornella Martino, Ivan 2016-09-01 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 complete Betti diagrams of the Veronese rings 𝕂[x, y, z](d), for d = 4, 5, and 𝕂[x, y, z, u](3). application/pdf https://folia.unifr.ch/global/documents/305125 https://folia.unifr.ch/documents/305125/files/mar_svm.pdf eng info:eu-repo/semantics/altIdentifier/doi/10.1080/00927872.2015.1027389 info:eu-repo/semantics/openAccess License undefined Communications in Algebra. - 2016, vol. 44, no. 9, p. 3890–3906 Betti Numbers Hilbert Series Pile simplicial complex Veronese Modules info:eu-repo/classification/udc/51 Syzygies of the Veronese modules http://purl.org/coar/resource_type/c_6501