{
  "abstract": "For $r> 2$, we study the moduli space parameterising fixed degree morphisms $\\mathbb P^r\\to X$ where $X$ is a smooth hypersurface of low degree. More precisely, we prove the following result: let $n\\geq 2, e\\geq 1$ and $X\\subset \\mathbb P^{n-1}$ a smooth degree $d\\geq 2$ hypersurface over an algebraically closed field of characteristic zero or greater than $d$, then $\\mathrm{Mor}_e(\\mathbb P^r, X)$ is irreducible of the expected dimension if \\[ n> 2^d(d-1)\\binom{de+r-1}{r-1}. \\] Our result extends the result of Browning-Yamagishi for $r=2$ via multiblock Weyl differencing.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20783",
  "author_total": 1,
  "authors": [
    {
      "name": "Hrishabh Mishra"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bvyyh6an0hwt9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20783",
  "fulltext_url": null,
  "id": "bvyyh6an0hwt9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20783",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7213591294",
  "pdf_url": "https://arxiv.org/pdf/2609.20783",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bvyyh6an0hwt9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.20783",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20783"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Morphism spaces on low degree hypersurfaces",
  "title_text": "Morphism spaces on low degree hypersurfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/bvyyh6an0hwt9",
  "venue": "arXiv",
  "versions": []
}