{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.38821",
  "author_total": 2,
  "authors": [
    {
      "name": "Benjamin Mascuch"
    },
    {
      "name": "Montserrat Teixidor i Bigas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cqmeap1jqzqxq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.38821",
  "fulltext_url": null,
  "id": "cqmeap1jqzqxq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.38821",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7215132828",
  "pdf_url": "https://arxiv.org/pdf/2609.38821",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cqmeap1jqzqxq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2609.38821",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.38821"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Divisors and harmonic morphisms on metric graphs of pseudocompact type",
  "title_text": "Divisors and harmonic morphisms on metric graphs of pseudocompact type",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/cqmeap1jqzqxq",
  "venue": "arXiv",
  "versions": []
}