Discrete behavior of Seshadri constants on surfaces

Abstract

Working over C , 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 P 2 and new results about ample divisors on blow ups of P 2 at general points.