Asymptotic syzygies of Stanley-Reisner rings of iterated subdivisions

Conca, Aldo; Juhnke-Kubitzke, Martina; Welker, Volkmar

doi:10.1090/tran/7149

Asymptotic syzygies of Stanley-Reisner rings of iterated subdivisions
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by Aldo Conca, Martina Juhnke-Kubitzke and Volkmar Welker PDF

Trans. Amer. Math. Soc. 370 (2018), 1661-1691 Request permission

Abstract:

Inspired by recent results of Ein, Lazarsfeld, Erman and Zhou on the non-vanishing of Betti numbers of high Veronese subrings, we describe the behavior of the Betti numbers of Stanley-Reisner rings associated with iterated barycentric or edgewise subdivisions of a given simplicial complex. Our results show that for a simplicial complex $\Delta$ of dimension $d-1$ and for $1\leq j\leq d-1$ the number of $0$’s in the $j^{\text {th}}$ linear strand of the minimal free resolution of the $r^{\text {th}}$ barycentric or edgewise subdivision is bounded above only in terms of $d$ and $j$ (and independently of $r$).

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