  Associated to an arrangement of projective hyperplanes A is the module D(A),
which consists of derivations tangent to A. We study D(A) when A is a
configuration of lines in the projective plane. 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(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
Terao's conjecture.
