Linear syzygies of Stanley-Reisner ideals - Reiner, V; Welker, V (MATHEMATICA SCANDINAVICA, 2001)
We give an elementary description of the maps in the linear strand of the minimal free resolution of a square-free monomial ideal, that is, the Stanley-Reisner ideal associated to a simplicial complex Δ. The description is in terms of the homology of the canonical Alexander dual complex Δ^*. As applications we are able to prove for monomial ideals and j=1 a conjecture of J. Herzog giving lower bounds on the number of i-syzygies in the linear strand of j^th-syzygy modules show that the maps in the linear strand can be written using only ± 1 coefficients if Δ^* is a pseudomanifold exhibit an example where multigraded maps in the linear strand cannot be written using only ± 1 coefficients compute the entire resolution explicitly when Δ^* is the complex of independent sets of a matroid