{
  "abstract": "Given a principally polarized abelian variety, we give a sufficient condition for the van Geemen-van der Geer locus $Γ_{00}$ to be positive dimensional. Along the way, we prove a sharp Castelnuovo-type inequality for hyperelliptic curves on abelian varieties, and characterize the cases in which we have equality. These results are consequences of a general relation between Seshadri constants and the surjectivity of high order Gauß-Wahl maps on curves inside abelian varieties, which we also prove. Applying such relation to Abel-Jacobi curves we obtain new results about the surjectivity of higher Gauß-Wahl maps on smooth curves, sharpening a previous result of Bertram, Ein and Lazarsfeld. In the process, we discuss further questions and conjectures.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.09418",
  "author_total": 1,
  "authors": [
    {
      "name": "Nelson Alvarado"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cpb6znf27ncgh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.09418",
  "fulltext_url": null,
  "id": "cpb6znf27ncgh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.09418",
  "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"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7164006281",
  "pdf_url": "https://arxiv.org/pdf/2606.09418",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cpb6znf27ncgh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2606.09418",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.09418"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Seshadri constants and hyperelliptic curves on abelian varieties",
  "title_text": "Seshadri constants and hyperelliptic curves on abelian varieties",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/cpb6znf27ncgh",
  "venue": "arXiv",
  "versions": []
}