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Stable cuspidal curves and the integral Chow ring of $\mkern5mu\overline{\mkern-5mu\mathcal{M}\mkern-2mu}\mkern2mu_{2,1}$

Andrea Di Lorenzo, Michele Pernice and Angelo Vistoli

Geometry & Topology 28 (2024) 2915–2970
Abstract

We introduce the moduli stack ~g,n of n–marked stable at most cuspidal curves of genus g and we use it to determine the integral Chow ring of ¯2,1. Along the way, we also determine the integral Chow ring of ¯1,2.

Keywords
Chow rings, moduli of curves, stacks, intersection theory
Mathematical Subject Classification
Primary: 14C15, 14D23, 14H10
References
Publication
Received: 10 January 2022
Revised: 22 August 2022
Accepted: 24 September 2022
Published: 21 October 2024
Proposed: Dan Abramovich
Seconded: Mark Gross, Jim Bryan
Authors
Andrea Di Lorenzo
Department of Mathematics
Humboldt-Universität zu Berlin
Berlin
Germany
Dipartimento di Matematica
Università di Pisa
Pisa
Italy
Michele Pernice
Scuola Normale Superiore
Pisa
Italy
Department of Mathematics
KTH Stockholm
Stockholm
Sweden
Angelo Vistoli
Scuola Normale Superiore
Pisa
Italy

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