Stable cohomology of moduli spaces of hyperelliptic curves on Hirzebruch surfaces

Abstract

We compute the stable cohomology of moduli spaces of hyperelliptic curves of a fixed genus embedded on a fixed Hirzebruch surface. We also describe these moduli spaces of embedded hyperelliptic curves in terms of moduli spaces of pointed non-embedded hyperelliptic curves.

v2: to be published in Pure and Applied Mathematics Quarterly