Syzygies of the Veronese modules

Greco, Ornella; Martino, Ivan

doi:10.1080/00927872.2015.1027389

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Journal article

Syzygies of the Veronese modules

Greco, Ornella Department of Mathematics, Royal Institute of Technology, Stockholm, Sweden
Martino, Ivan Départment de Mathématiques, Université de Fribourg, Fribourg, Switzerland

01.09.2016

Published in:

Communications in Algebra. - 2016, vol. 44, no. 9, p. 3890–3906

English 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).

Faculty

Faculté des sciences et de médecine

Department

Département de Mathématiques

Language