On accumulation points of volumes of log surfaces

Abstract

Let be a set satisfying the descending chain condition. We show that every accumulation point of volumes of log canonical surfaces with coefficients in can be realized as the volume of a log canonical surface with big and nef and with coefficients in in such a way that at least one coefficient lies in . As a corollary, if , then all accumulation points of volumes are rational numbers. This proves a conjecture of Blache. For the set of standard coefficients we prove that the minimal accumulation point is between and .