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Higher genus modular graph functions, string invariants, and their exact asymptotics. (English) Zbl 1430.14072

Le premier but de cet article est de construire des fonctions graphes modulaires sur les surfaces de Riemann compactes de genre arbitraire. Ces constructions sont données dans la section 2.
Le second but de cet article est de déterminer le comportement des fonctions graphes modulaires au voisinage du diviseur de la compactification de Deligne-Mumford paramètrant les courbes avec un nœud non séparant. En particulier, le théorème 1 donne le comportement de la fonction d’Arakelov-Green et le théorème 2 de l’invariant de Kawazumi-Zhang. Deux autres familles de fonctions graphes modulaires sont traitées dans les théorèmes 3 et 4.

MSC:

14H81 Relationships between algebraic curves and physics
05C10 Planar graphs; geometric and topological aspects of graph theory
30F60 Teichmüller theory for Riemann surfaces
14G40 Arithmetic varieties and schemes; Arakelov theory; heights
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