{
  "abstract": "We give an obstruction to the existence of bundles $\\mathcal E$ on a smooth $n$-dimensional polarized variety such that $\\mathcal E$ is $a$-regular and $\\mathcal E^*(K_X+(n+1)H)$ is $b$-regular. In particular, this gives an obstruction to the existence of weakly Ulrich bundles. Using these obstructions and some recent examples of \\cite{a1} in dimension $2$, we prove that for any $n \\ge 2$ there exist many smooth $n$-dimensional varieties $X$ with a very ample line bundle $H$, such that there is no weakly Ulrich bundle for $(X,H)$, no ordinary instanton bundle with bounded quantum number, no non-ordinary $μ$-semistable instanton bundle with bounded quantum number and no bundle with supernatural cohomology and bounded roots.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.36231",
  "author_total": 2,
  "authors": [
    {
      "name": "Ozhan Genc"
    },
    {
      "name": "Angelo Felice Lopez"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/daqgvcbwrghmn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.36231",
  "fulltext_url": null,
  "id": "daqgvcbwrghmn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.36231",
  "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": "W7224109494",
  "pdf_url": "https://arxiv.org/pdf/2610.36231",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/daqgvcbwrghmn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.36231",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.36231"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the existence of polarized varieties without weakly Ulrich bundles",
  "title_text": "On the existence of polarized varieties without weakly Ulrich bundles",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/daqgvcbwrghmn",
  "venue": "arXiv",
  "versions": []
}