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

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.