Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 20 (2024), 088, 16 pages      arXiv:2112.10182      https://doi.org/10.3842/SIGMA.2024.088

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

Received January 05, 2022, in final form August 27, 2024; Published online October 06, 2024

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.

Key words: moduli space of curves; tautological relations; cohomological field theories.

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