{
  "abstract": "Counterexamples to the Eisenbud-Schreyer conjecture on the existence of Ulrich bundles have appeared recently (see Anghel [A1] and the third author [Lo]). As weakly Ulrich bundles are a useful generalization of Ulrich ones, in this paper, we classify smooth surfaces $S\\subseteq \\mathbb P^N$ with weakly Ulrich tangent bundle. They are Del-Pezzo surfaces of degree at least 5 and we classify the possible embeddings. An interesting feature is the appearance of two infinite series of polarizations, which is quite different from the Ulrich case [BMPT, LR]. We also achieve the classification of surfaces with initialized aCM tangent bundles and, as a consequence, of surfaces with almost Ulrich tangent bundles.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04739",
  "author_total": 3,
  "authors": [
    {
      "name": "Debojyoti Bhattacharya"
    },
    {
      "name": "Ozhan Genc"
    },
    {
      "name": "Angelo Felice Lopez"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e5tk9e0n2ap6y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04739",
  "fulltext_url": null,
  "id": "e5tk9e0n2ap6y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04739",
  "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": "W7220686330",
  "pdf_url": "https://arxiv.org/pdf/2610.04739",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e5tk9e0n2ap6y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.04739",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04739"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the classification of polarized surfaces with weakly Ulrich or initialized aCM tangent bundles",
  "title_text": "On the classification of polarized surfaces with weakly Ulrich or initialized aCM tangent bundles",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/e5tk9e0n2ap6y",
  "venue": "arXiv",
  "versions": []
}