{
  "abstract": "Let $X$ be a fixed complex K3 surface and let $0\\neα\\in\\overline{Kah_X}$ be a $(1,1)$-class on the boundary of the Kähler cone with $α^2=0$. We build a novel connection between two seemingly unrelated, intensively studied problems: the rigidity of a closed positive current in the class $α$ and the collapse geometry of a sequence of Ricci-flat Kähler metrics in the Kähler class $α+tκ$ as $t\\to 0^+$. More precisely, we prove that $α$ contains a unique closed positive $(1,1)$-current if and only if the Ricci-flat metrics in class $α+tκ$ collapse to a point in the Gromov--Hausdorff sense. Then we exhibit the first example of a nonrigid irrational nef class $α$ on a Kummer surface, which answers a question of Filip--Tosatti and Sibony--Soldatenkov--Verbitsky. We also construct many new examples of rigid nef classes on hyperkähler manifolds, which extend the work of Filip--Tosatti and Sibony--Soldatenkov--Verbitsky.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33632",
  "author_total": 2,
  "authors": [
    {
      "name": "Xin Fu"
    },
    {
      "name": "Zexuan Ouyang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5g2b4ktczgvg8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33632",
  "fulltext_url": null,
  "id": "5g2b4ktczgvg8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33632",
  "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"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7214756302",
  "pdf_url": "https://arxiv.org/pdf/2609.33632",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5g2b4ktczgvg8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.33632",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33632"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Rigid and Nonrigid Isotropic Nef Classes on K3 Surfaces",
  "title_text": "Rigid and Nonrigid Isotropic Nef Classes on K3 Surfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/5g2b4ktczgvg8",
  "venue": "arXiv",
  "versions": []
}