Rational curves and Seshadri constants on Enriques surfaces

Abstract

We prove that classes of rational curves on very general Enriques surfaces are always $2$-divisible. As a consequence, we prove that the Seshadri constant of any big and nef line bundle on a very general Enriques surface coincides with the value of the $\varphi$-function introduced by Cossec.

11 pages. Minor changes. Final version, encorporating referee's corrections

References in corpus (4)

• Seshadri constants on algebraic surfaces
• Irreducible unirational and uniruled components of moduli spaces of polarized Enriques surfaces
• A note on Severi varieties of nodal curves on Enriques surfaces
• Nonemptiness of Severi varieties on Enriques surfaces

Cited by in corpus (1)

• Nodal rational curves on Enriques surfaces of base change type