Irreducible unirational and uniruled components of moduli spaces of polarized Enriques surfaces

Abstract

We prove that infinitely many irreducible components of the moduli space of polarized Enriques surfaces are unirational (resp. uniruled), characterizing them in terms of decompositions of the polarization as an effective sum of isotropic classes. In particular, this applies to components of arbitrarily large genus g and phi -invariant of the polarization.