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
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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
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- English
- Classification
- Mathematics
- License
- License undefined
- Identifiers
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- RERO DOC 277694
- DOI 10.1080/00927872.2015.1027389
- Persistent URL
- https://folia.unifr.ch/unifr/documents/305125
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