  The Castelnuovo-Mumford regularity of the Jacobian algebra and of the graded
module of derivations associated to a general curve arrangement in the complex
projective plane are studied. The key result is an addition-deletion type
result, similar to results obtained by H. Schenck, H. Terao, S. Tohaneanu and
M. Yoshinaga, but in which no quasi homogeneity assumption is needed.
