Rational cohomology of \bar R_2 (and \bar S_2)

TL;DR

This paper computes the rational cohomology rings of the moduli spaces of Prym and spin curves of genus 2, providing corrected and detailed algebraic topological information about these spaces.

Contribution

It offers the first complete computation of the rational cohomology ring of ar R_2 and revises previous results for ar S_2, correcting earlier errors.

Findings

Rational cohomology ring of ar R_2 computed.

Rational cohomology ring of ar S_2 recomputed and corrected.

Provides algebraic topological insights into genus 2 moduli spaces.

Abstract

We compute the rational cohomology ring of \bar R_2, the (compactified) moduli space of Prym curves of genus 2. We also recompute the rational cohomology ring of \bar S_2, the moduli space of spin curves of genus 2, thereby correcting some errors made in an article by G. Bini and C. Fontanari, containing a computation of the same ring.