{
  "abstract": "Let f ∈ C[x, y] be a trinomial and let g ∈ C[x, y] be a sparse polynomial with N monomials (N ≥ 1). We address the problem of bounding the local intersection multiplicity of the bivariate polynomial system f = g = 0 at an isolated root q ∈ (C * )^ 2 only in terms of N . Our main result establishes that the local multiplicity of the system at any isolated solution q ∈ (C * ) ^2 is at most (N -1)(N +2)/ 2 , independently of the degrees of f and g. Furthermore, we know that this bound is sharp for N = 3.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35037",
  "author_total": 1,
  "authors": [
    {
      "name": "Jean Mousseau"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4m4g9d5cc6p9m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35037",
  "fulltext_url": null,
  "id": "4m4g9d5cc6p9m",
  "issns": [],
  "landing_url": "https://hal.science/hal-05837591v2",
  "language": "en",
  "licence": "CC-BY-NC-4.0",
  "licence_label": "CC BY-NC 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AC"
    ],
    [
      "arxiv",
      "math.AG"
    ],
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      "hal",
      "0.math"
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      "hal",
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    [
      "openalex",
      "1703|Polynomial and algebraic computation"
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  ],
  "openalex": "W7223839616",
  "pdf_url": "https://hal.science/hal-05837591/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4m4g9d5cc6p9m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:02Z",
      "native_id": "hal-05837591",
      "source": "hal",
      "url": "https://hal.science/hal-05837591v2"
    },
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.35037",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35037"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Intersection multiplicity of a sparse curve and a trinomial curve",
  "title_text": "Intersection multiplicity of a sparse curve and a trinomial curve",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/4m4g9d5cc6p9m",
  "venue": "HAL",
  "versions": []
}