Minimal free resolutions that are not supported by a CW-complex (Q2470394)

Given a simplicial complex \(\Omega\) with at least 2 vertices its nearly scarf ideal \(J_{\Omega}\) is the ideal in the ring \(R=K[\{x_{F}: F \in \Omega, F \neq \emptyset \}]\) generated by the monomials \(m_{v}=\prod_{F \not\ni v}x_{F}\) as \(v\) ranges through the vertices of \(\Omega\). Using these ideals the author construct monomial ideals whose minimal free resolutions are not supported by any CW-complex. Their existence answers negatively the question of whether every monomial ideal admits a minimal cellular resolution.