Restrictions on Seshadri Constants on Surfaces

Abstract

Starting with the pioneering work of Ein and Lazarsfeld [9] restrictions on values of Seshadri constants on algebraic surfaces have been studied by many authors [2,5,10,12,18,20,22,24]. In the present note we show how approximation involving continued fractions combined with recent results of Küronya and Lozovanu on Okounkov bodies of line bundles on surfaces [13,14] lead to effective statements considerably restricting possible values of Seshadri constants. These results in turn provide strong additional evidence to a conjecture governing the Seshadri constants on algebraic surfaces with Picard number $1$.