Seshadri constants on surfaces of general type

We study Seshadri constants of the canonical bundle on minimal surfaces of general type. First, we prove that if the Seshadri constant ε(K _X , x) is between 0 and 1, then it is of the form (m − 1)/m for some integer m ≥ 2. Secondly, we study values of ε(K _X , x) for a very general point x and show that small values of the Seshadri constant are accounted for by the geometry of X.