Cohomology of the moduli space of degree two Enriques surfaces

TL;DR

This paper calculates the intersection Betti numbers of the GIT model of the moduli space of degree two Enriques surfaces using Kirwan's method, involving stratification and resolution of singularities.

Contribution

It applies and extends Kirwan's cohomological techniques to a specific class of algebraic surfaces, providing explicit Betti number computations.

Findings

Computed intersection Betti numbers for the moduli space

Developed a stratification approach for the GIT quotient

Performed a partial resolution of singularities

Abstract

We compute the intersection Betti numbers of the GIT model of the moduli space of numerically polarized Enriques surfaces of degree 2. The strategy of the cohomological calculation relies on a general method developed by Kirwan to compute the cohomology of GIT quotients of projective varieties, based on the equivariantly perfect stratification of the unstable points studied by Hesselink and others and a partial resolution of singularities, called Kirwan blow-up.