{
  "abstract": "Let $G=\\operatorname{Gr}(k,V)$ be a complex Grassmannian in its Pl$ü$cker embedding, and let $Y_E$ be a general codimension-$r$ linear section. We study the open Hilbert scheme $R_2(Y_E)$ of smooth conics using the kernel and span of a conic. These define a flag variety $B=\\operatorname{Fl}(k-2,k+2;V)$ and a relative Grassmannian of three-planes in a rank-six bundle. For $0\\le r\\le3$, we prove that $R_2(Y_E)$ is nonempty, smooth, irreducible and rational of dimension $e=2\\dim V+k(\\dim V-k)-3-3r$, with birational model $B\\times\\operatorname{Gr}(3,6-r)$. For $r\\ge4$, a general-position argument gives a componentwise birational correspondence with a rank-three degeneracy locus and two smooth projective incidence resolutions. Every component meets the locus of smooth minimal-envelope conics; no additional density assumption is needed for general $E$. If $0\\le e\\le r$, the degeneracy locus itself is smooth. In dimension zero we obtain a top Chern class formula, recovering the known counts $1225$ and $1176$ by exact localization.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04727",
  "author_total": 1,
  "authors": [
    {
      "name": "Zheyuan Fu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5gqgtmnphr5vb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04727",
  "fulltext_url": null,
  "id": "5gqgtmnphr5vb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04727",
  "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": "W7211883532",
  "pdf_url": "https://arxiv.org/pdf/2609.04727",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5gqgtmnphr5vb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.04727",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04727"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Moduli of Conics on General Plucker Linear Sections of Grassmannians",
  "title_text": "Moduli of Conics on General Plucker Linear Sections of Grassmannians",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/5gqgtmnphr5vb",
  "venue": "arXiv",
  "versions": []
}