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A formula for the Euler characteristic of \(\overline{\mathcal M}_{2,n}\). (English) Zbl 1056.14505

Summary: We compute the generating function for the Euler characteristic of the Deligne-Mumford compactification of the moduli space of smooth \(n\)-pointed genus 2 curves. The proof relies on quite elementary methods, such as the enumeration of the graphs involved in a suitable stratification of \(\overline{\mathcal M}_{2,n}\).

MSC:

14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)
05C30 Enumeration in graph theory
14H10 Families, moduli of curves (algebraic)
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