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arXiv · 1411.3695

Asymptotic syzygies of Stanley-Reisner rings of iterated subdivisions

Aldo Conca·Martina Juhnke-Kubitzke·Volkmar Welker
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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 behaviour 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 the j-th linear strand of the minimal free resolution of the r-th barycentric or edgewise subdivision is bounded above only in terms of $d$ and $j$ (and independently of $r$).

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Aldo Conca, Martina Juhnke-Kubitzke, Volkmar Welker. 2014-11-13. Asymptotic syzygies of Stanley-Reisner rings of iterated subdivisions. https://arxiv.org/abs/1411.3695

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