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}
}
  • O. Greco, I. Martino
  • 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
    10 Citations
    Cohen-Macaulay Property of pinched Veronese Rings
    • 2
    • PDF
    Computing graded Betti tables of toric surfaces
    • 10
    • PDF
    Conjectures and Computations about Veronese Syzygies
    • 2
    • PDF
    Efficiency Axioms for simplicial complexes
    • 1
    • PDF
    Cooperative games on simplicial complexes
    • Ivan Martino
    • Computer Science, Mathematics
    • Discret. Appl. Math.
    • 2021
    • 2
    • PDF
    Free Resolutions from Involutive Bases
    • 1

    References

    SHOWING 1-10 OF 26 REFERENCES
    Linear Free Resolutions and Minimal Multiplicity
    • 435
    • PDF
    Semigroup rings and simplicial complexes
    • 58
    • PDF
    Syzygies of affine toric varieties
    • 31
    The Koszul property of pinched Veronese varieties
    • 3
    • PDF
    Syzygies of Veronese Embeddings
    • 55
    • PDF
    Cohen-Macaulay Rings
    • 2,357
    The Veronese construction for formal power series and graded algebras
    • 46
    • PDF
    Canonical Modules of Semigroup Rings and a Conjecture of Reiner
    • X. Dong
    • Mathematics, Computer Science
    • Discret. Comput. Geom.
    • 2002
    • 7
    • PDF