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Description

Inspired by 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 in 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 \(r\)). This is joint work with Aldo Conca and Volkmar Welker.