On the Picard Group of the Moduli Space of Curves via $r$-Spin Structures

Abstract

In this paper, we obtain explicit expressions for Pandharipande-Pixton-Zvonkine relations in the second rational cohomology of ${\overline{\mathcal{M}}}_{g,n}$ and comparing the result with Arbarello-Cornalba's theorem we prove Pixton's conjecture in this case.