On the rational cohomology of moduli spaces of curves with level structures

Abstract

We investigate low degree rational cohomology groups of smooth compactifications of moduli spaces of curves with level structures. In particular, we determine $H^k(\sgbar, \Q)$ for $g\ge 2$ and $k\le 3$, where $\sgbar$ denotes the moduli space of spin curves of genus $g$.

Final version accepted for publication on Geometriae Dedicata

References in corpus (2)

• The second rational homology group of the moduli space of curves with level structures
• Divisors in the moduli spaces of curves