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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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Cite

BibTeXRIS
BibTeX
@misc{mascuch2026divisors,
  title = {{Divisors and harmonic morphisms on metric graphs of pseudocompact type}},
  author = {Benjamin Mascuch and Montserrat Teixidor i Bigas},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.38821},
  eprint = {2609.38821},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.38821},
}
RIS
TY  - UNPB
TI  - Divisors and harmonic morphisms on metric graphs of pseudocompact type
AU  - Benjamin Mascuch
AU  - Montserrat Teixidor i Bigas
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.38821
UR  - https://arxiv.org/abs/2609.38821
AB  - 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.
ER  -