Stable cuspidal curves and the integral Chow ring of ℳ 2,1

Di Lorenzo, Andrea¹ ; Pernice, Michele² ; Vistoli, Angelo³

¹ Department of Mathematics, Humboldt-Universität zu Berlin, Berlin, Germany, Dipartimento di Matematica, Università di Pisa, Pisa, Italy
² Scuola Normale Superiore, Pisa, Italy, Department of Mathematics, KTH Stockholm, Stockholm, Sweden
³ Scuola Normale Superiore, Pisa, Italy

Geometry & topology, Tome 28 (2024) no. 6, pp. 2915-2970.

Résumé

We introduce the moduli stack ${\widetilde{\mathcal{ℳ}}}_{g,n}$ of $n$–marked stable at most cuspidal curves of genus $g$ and we use it to determine the integral Chow ring of ${\overline{\mathcal{ℳ}}}_{2,1}$. Along the way, we also determine the integral Chow ring of ${\overline{\mathcal{ℳ}}}_{1,2}$.

Détail

DOI : 10.2140/gt.2024.28.2915

Keywords: Chow rings, moduli of curves, stacks, intersection theory

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