The rationality of the moduli spaces of Coble surfaces and of nodal Enriques surfaces

TL;DR

This paper proves that the coarse moduli spaces of Coble surfaces and nodal Enriques surfaces are rational over the complex numbers, establishing their geometric simplicity.

Contribution

It demonstrates the rationality of the moduli spaces for these specific algebraic surfaces, a previously unresolved problem.

Findings

Moduli spaces of Coble surfaces are rational.

Moduli spaces of nodal Enriques surfaces are rational.

The proof applies over the complex numbers.

Abstract

We prove the rationality of the coarse moduli spaces of Coble surfaces and of nodal Enriques surfaces over the field of complex numbers.