# On K^2 for stable surfaces

V. Alexeev proved in 1994 that the set *S* of self-intersections of the canonical class of stable surfaces satisfies the descending chain condition, this is, any monotone sequence is increasing. (This set *S* is a subset of the positive rational numbers.) In particular *S* has a minimum, and it may have accumulation points. I will discuss what is known about *S*, certain new theorems on accumulation points, and open questions. This is a joint work with José Ignacio Yáñez.