A remark on the rational cohomology of $\bar{S}_{1,n}$
  We focus on the rational cohomology of Cornalba's moduli space of spin curves of genus 1 with $n$ marked points. In particular, we show that both its first and its third cohomology group vanish and the second cohomology group is generated by boundary classes. 
Gilberto Bini and Claudio Fontanari