{
  "abstract": "Let u : V → W be a morphism of algebraic varieties. Given an integer m or m = ∞, we prove that the set of y ∈ W such that u -1 (y) has size m, is a constructible set. We also show that this set is locally closed when W is normal and u is finite.\n\n.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09128",
  "author_total": 1,
  "authors": [
    {
      "name": "Abdelkader Mokkadem"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8keef2qnxaxbm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09128",
  "fulltext_url": null,
  "id": "8keef2qnxaxbm",
  "issns": [],
  "landing_url": "https://hal.science/hal-05743087v2",
  "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.AG"
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      "hal",
      "0.math"
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      "openalex",
      "2608|Algebraic Geometry and Number Theory"
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  "openalex": "W7212041858",
  "pdf_url": "https://hal.science/hal-05743087/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8keef2qnxaxbm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:33Z",
      "native_id": "hal-05743087",
      "source": "hal",
      "url": "https://hal.science/hal-05743087v2"
    },
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.09128",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09128"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the size of the fibers of a morphism of algebraic varieties",
  "title_text": "On the size of the fibers of a morphism of algebraic varieties",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/8keef2qnxaxbm",
  "venue": "HAL",
  "versions": []
}