On property of complements of an algebraic curve with at least 4 irreducible components in P²

Abstract

For the manifold M := P² - A(l) (l ≥ 4) where A(l) is an algebraic curve with l irreducible components, the notion that M is of log general type, measure hyperbolic and Δ_M is a curve or empty set, where Δ_M is the degeneracy locus of the Kobayashi pseudodistance d_M on M, coincide with each other.