Nancy Abdallah: Nets in P^2 and Alexander Duality

Abstract.

A net in \(\mathbb{P}^2\) is a configuration of lines \(A\) and points \(X\) satisfying certain incidence properties. For a matroid \(M\) and rank \(r\), we associate monomial ideal (a monomial variant of the Orlik-Solomon ideal) to the set of flats of \(M\) or rank at most \(r\). In the context of line arrangements in the projective plane, applying Alexander duality to the resulting ideal yields insight into the combinatorial structure of notes.