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 ℳ¯𝑔,ₙ, and, comparing the result with Arbarello-Cornalba's theorem, we prove Pixton's conjecture in this case.