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

Abstract: We give an explicit description of the irreducible components of the moduli spaces of polarized Enriques surfaces in terms of decompositions of the polarization as an effective sum of isotropic classes. We prove that infinitely many of these components are unirational (resp. uniruled). In particular, this applies to components of arbitrarily large genus $g$ and $\phi$-invariant of the polarization.