Danil Gubarevich, “On the Picard Group of the Moduli Space of Curves via <nobr>$r$</nobr>-Spin Structures”, SIGMA, 2024, Volume 20,088, 16 pp.

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

Danil Gubarevich^ab

^a Laboratoire de Mathématiques de Versailles, UFR des Sciences, Université de Versailles Saint-Quentin en Yvelines, 45 avenue des États-Unis, 78035 Versailles, France
^b Faculty of Mathematics, National Research University Higher School of Economics, 6 Usacheva Str., 119048 Moscow, Russia

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.

Keywords: moduli space of curves, tautological relations, cohomological field theories.

MSC: 14H10, 14N35

Received: January 5, 2022; in final form August 27, 2024; Published online October 6, 2024

Language: English

DOI: 10.3842/SIGMA.2024.088