{
  "abstract": "For every integer $n\\ge3$, we construct a smooth projective manifold $X$ of complex dimension $n$ whose canonical bundle is not pseudoeffective, or equivalently, which is uniruled, but every Kähler metric has negative total scalar curvature. In particular, $X$ admits no Kähler metric of positive scalar curvature, while it admits a Riemannian metric of positive scalar curvature. Thus the equivalence between uniruledness and the existence of a Kähler metric with positive scalar curvature holds in complex dimensions one and two, but fails in higher dimensions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.26640",
  "author_total": 2,
  "authors": [
    {
      "name": "Zehao Sha"
    },
    {
      "name": "Jian Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4yy8b2hxgaxmr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.26640",
  "fulltext_url": null,
  "id": "4yy8b2hxgaxmr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.26640",
  "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": "W7214075150",
  "pdf_url": "https://arxiv.org/pdf/2609.26640",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4yy8b2hxgaxmr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.26640",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.26640"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Uniruledness and the sign of total scalar curvature",
  "title_text": "Uniruledness and the sign of total scalar curvature",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/4yy8b2hxgaxmr",
  "venue": "arXiv",
  "versions": []
}