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

2009/08/13 by Bini, Gilberto, Fontanari, Claudio
#14H10 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0908.1853

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 ≥ 2 and k ≤ 3, where \sgbar denotes the moduli space of spin curves of genus g.

Related

• The stable cohomology of the moduli space of curves with level structures
• Rational cohomology of R₂ (and S₂)
• The cohomology of the moduli space of curves at infinite level
• Calculating cohomology groups of moduli spaces of curves via algebraic geometry
• On the geometry of S₂