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

TL;DR

This paper explicitly describes the irreducible components of moduli spaces of polarized Enriques surfaces, showing many are unirational or uniruled, including those with large genus and polarization invariants.

Contribution

It provides a detailed description of moduli space components for polarized Enriques surfaces and proves their unirationality or uniruledness for infinitely many cases.

Findings

Many components are unirational or uniruled.

Applicability to components with arbitrarily large genus and polarization invariants.

Explicit description via decompositions of polarization as sums of isotropic classes.

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.