Asymptotic syzygies of Stanley-Reisner rings of iterated subdivisions

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 Δ \Delta of dimension d − 1 d-1 and for 1 ≤ j ≤ d − 1 1\leq j\leq d-1 the number of 0 0 ’s in the j th j^{\text {th}} linear strand of the minimal free resolution of the r th r^{\text {th}} barycentric or edgewise subdivision is bounded above only in terms of d d and j j (and independently of r r ).