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 Delta of dimension d-1 and for 1 <= j <= d - 1 the number of 0's in the jth linear strand of the minimal free resolution of the rth barycentric or edgewise subdivision is bounded above only in terms of d and j (and independently of r).