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arXiv · 2606.17911

Single-valued polylogarithms for higher genera

Konstantin Baune·Johannes Broedel·Yannis Moeckli
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Abstract

We extend the construction of single-valued polylogarithms at genus one from arXiv:2511.15240 to once-punctured Riemann surfaces of higher genera. The resulting functions have a trivial monodromy representation with respect to the fundamental group, hence they descend to well-defined functions on the surface. Our construction of single-valued polylogarithms is based on Enriquez' connection and relates them to the polylogarithms from D'Hoker-Hidding-Schlotterer. Finally, we identify the Arakelov Green's function within our framework.

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Konstantin Baune, Johannes Broedel, Yannis Moeckli. 2026-06-16. Single-valued polylogarithms for higher genera. https://arxiv.org/abs/2606.17911

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