Elementary modifications and line configurations in P^2

Abstract

Associated to a projective arrangement of hyperplanes $\mathcal{A}$ in P^n is the module D$(\mathcal{A})$, which consists of derivations tangent to $\mathcal{A}$. We study D$(\mathcal{A})$ when $\mathcal{A}$ is a configuration of lines in P^2. In this setting, we relate the deletion/restriction construction used in the study of hyperplane arrangements to elementary modifications of bundles. This allows us to obtain bounds on the Castelnuovo-Mumford regularity of D$(\mathcal{A})$. We also give simple combinatorial conditions for the associated bundle to be stable, and describe its jump lines. These regularity bounds and stability considerations impose constraints on Teraos conjecture.