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arXiv · 2609.38821

Divisors and harmonic morphisms on metric Graphs of pseudocompact type

Benjamin Mascuch·Montserrat Teixidor i Bigas
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Abstract

A metric graph is of pseudocompact type if identifying parallel edges produces a tree. We give a constructive proof that, for such graphs, divisorial $d$-gonality is equivalent to the existence of a degree $d$ harmonic morphism to a tree. This mirrors the algebraic correspondence, for curves of compact type, between limit linear series of dimension one and admissible covers. We also deduce lifting results for positive-rank divisors, with a genus-preserving refinement when identifying parallel edges produces a path. Finally, we study the Brill-Noether theory in the path case.

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Benjamin Mascuch, Montserrat Teixidor i Bigas. 2026-09-30. Divisors and harmonic morphisms on metric Graphs of pseudocompact type. https://arxiv.org/abs/2609.38821

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