{
  "abstract": "We prove Mond's conjecture for $\\mathcal A$-finite corank-one map germs $(\\mathbb C^3,0)\\to(\\mathbb C^4,0)$: the $\\mathcal A_e$-codimension is at most the image Milnor number, with equality for quasihomogeneous germs. For a quasihomogeneous germ we determine the derivations of its image modulo the conductor fields, in terms of the double-point surface, its cross-cap curve and its normalisation. This yields a closed formula, depending only on the weights and degrees, for the Hilbert series of the graded $\\mathcal A_e$-normal space; its value at $t=1$ coincides with Ohmoto's formula for the image Milnor number, which comes from Segre--Schwartz--MacPherson Thom polynomials. For arbitrary germs we show that generic homogeneous corank-one germs of coprime degrees are $\\mathcal A$-finite in every source dimension, and apply the reduction theorem of Fernández de Bobadilla, Nuño-Ballesteros and Peñafort Sanchis. In every pair of nice dimensions this reduces Mond's conjecture for corank-one germs to an inequality for generic homogeneous germs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03331",
  "author_total": 1,
  "authors": [
    {
      "name": "Richard Rimanyi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1n6rjj97vyn2b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03331",
  "fulltext_url": null,
  "id": "1n6rjj97vyn2b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03331",
  "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": "W7220428013",
  "pdf_url": "https://arxiv.org/pdf/2610.03331",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1n6rjj97vyn2b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.03331",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03331"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Mond's conjecture for corank-one maps from $\\mathbb C^3$ to $\\mathbb C^4$",
  "title_text": "Mond's conjecture for corank-one maps from ℂ^3 to ℂ^4",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/1n6rjj97vyn2b",
  "venue": "arXiv",
  "versions": []
}