On Hodge Theory of Singular Plane Curves

Abstract

AbstractThe dimensions of the graded quotients of the cohomology of a plane curve complement U = ℙ2 \ C with respect to the Hodge filtration are described in terms of simple geometrical invariants. The case of curves with ordinary singularities is discussed in detail. We also give a precise numerical estimate for the difference between the Hodge filtration and the pole order filtration on H2(U,ℂ).