| Résume | Consider a sequence of smooth compact Riemann surfaces of genus g whose corresponding points in the moduli space Mg converge to a point in the Deligne–Mumford compactification. We consider the following question: what is the limit of the associated sequence of Arakelov-Bergman measures?
Combining graph theory, tropical non-archimedean geometry and Hodge theory, we obtain a full answer and a new compactification of the moduli spaces of curves. Joint work with Noema Nicolussi (École Polytechnique). |
