Rational curves and Seshadri constants on Enriques surfaces

Abstract

We prove that classes of rational curves on very general Enriques surfaces are always 2 2 -divisible. As a consequence, we compute the Seshadri constant of any big and nef line bundle on a very general Enriques surface, proving that it coincides with the value of the ϕ \phi -function introduced by Cossec [Math. Ann. 271 (1985), pp. 577–600].