CALABI-YAU METRICS WITH CONICAL SINGULARITIES ALONG LINE ARRANGEMENTS

Given a finite collection of lines Lj subset of CP2 together with real numbers 0 < beta(j) < 1 satisfying natural constraint conditions, we show the existence of a Ricci-flat Kahler metric g(RF) with cone angle 2 pi beta(j) along each line L-j asymptotic to a polyhedral Kahler cone at each multiple point. Moreover, we discuss a Chern-Weil formula that expresses the energy of gRF as a logarithmic Euler characteristic with points weighted according to the volume density of the metric.