We discuss applications of the Milnor-Thom Theorem, a result from AlgebraicGeometry concerning signs of polynomials, to the combinatorics of geometricconfigurations. In particular, we define an {it abstract lineconfiguration}, modelled on line configurations in $mathbb{R}^3$, and showthat there are many forbidden sub-configurations. We discuss theimplications for unavoidable "stacked" sets of lines via theErdH{o}s-Hajnal conjecture, and pose several open questions. Joint workwith Uli Wagner of ETH Z"{u}rich.