Boundness of log-canonical surfaces of general type (after Alexeev-Mori)

In the talk we discuss the proof of the theorem of Alexeev-Mori on the existence of a lower bound on the self-intersection of a log-canonical divisor of a log-canonical surface of general type. More precisely, the bound is given in the terms of an (arbitrary) subset of $\mathbb{R}$ containing the coefficients of the boundary and satisfying the descending chain condition.