Abstract
Let I⊂C[x,y,z] be an ideal of height 2 and minimally generated by three homogeneous polynomials of the same degree. If I is a locally complete intersection we give a criterion for C[x,y,z]/I to be arithmetically Cohen-Macaulay. Since the setup above is most commonly used when I=JF is the Jacobian ideal of the defining polynomial of a "quasihomogeneous" reduced curve Y=V(F) in P2, our main result becomes a criterion for freeness of such divisors. As an application we give an upper bound for the degree of the reduced Jacobian scheme when Y is a free rank 3 central essential arrangement, as well as we investigate the connections between the first syzygies on JF, and the generators of √JF.