Discrete behavior of Seshadri constants on surfaces

Working over image, we show that, apart possibly from a unique limit point, the possible values of multi-point Seshadri constants for general points on smooth projective surfaces form a discrete set. In addition to its theoretical interest, this result is of practical value, which we demonstrate by giving significantly improved explicit lower bounds for Seshadri constants on image and new results about ample divisors on blow ups of image at general points.