{
  "abstract": "We study a particular instance of the frame work from \\cite{Grieve:CM:Line:Slope:Stab}, building on earlier work of Arezzo-et-al \\cite{Arezzo:DellaVedova:LaNave}, Ross and Thomas \\cite{Ross:Thomas:2007}, \\cite{Ross:Thomas:2006} and others, which applies the theory of the Chow-Mumford line bundle to determine the Donaldson-Futaki invariant of deformation to the normal cone test configurations with respect to big and nef line bundles. In particular, here we consider the case of projective $n$-space blown-up along a linear subspace. Our main result arises as an application of \\cite[Theorem 1.1]{Grieve:CM:Line:Slope:Stab}. It establishes $\\K$-semistability of the deformation to the normal cone test configuration for the blow-up $\\PP(\\Osh_{\\PP^s}^{\\oplus r} \\oplus \\Osh_{\\PP^s}(1)) \\simeq \\operatorname{Bl}_{\\PP^{r-1}}(\\PP^s)$ along the exceptional divisor and with respect to the tautological line bundle $\\Osh_{\\PP(\\Osh_{\\PP^s}^{\\oplus r} \\oplus \\Osh_{\\PP^s}(1))}(1)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12319",
  "author_total": 1,
  "authors": [
    {
      "name": "Nathan Grieve"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3fyse73p0t8rd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12319",
  "fulltext_url": null,
  "id": "3fyse73p0t8rd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12319",
  "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"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7212819435",
  "pdf_url": "https://arxiv.org/pdf/2609.12319",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3fyse73p0t8rd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.12319",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12319"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Seshadri slope $\\K$-semistability for the blow-up of projective space along a linear subspace",
  "title_text": "Seshadri slope K-semistability for the blow-up of projective space along a linear subspace",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/3fyse73p0t8rd",
  "venue": "arXiv",
  "versions": []
}