  We study divisors in a complex manifold in view of the property that the
algebra of logarithmic differential operators along the divisor is generated by
logarithmic vector fields. We give a sufficient criterion for the property, a
simple proof of F.J. Calderon-Moreno's theorem that free divisors have the
property, a proof that divisors in dimension 3 with only isolated
quasi-homogeneous singularities have the property, an example of a non-free
divisor with non-isolated singularity having the property, an example of a
divisor not having the property, and an algorithm to compute the V-filtration
along a divisor up to a given order.
