  This is a short note on various results about the combinatorial properties of
line arrangements in terms of the Chern numbers of the corresponding log
surfaces. This resembles the study of the geography of surfaces of general
type. We prove some new results about the distribution of Chern slopes, we
prove a connection between their accumulation points and the accumulation
points of linear $H$-constants on the plane, and we present two open problems
in relation to geography over $\mathbb Q$ and over $\mathbb C$.
