{
  "abstract": "Let $X$ be a smooth projective variety of dimension $n$ over an algebraically closed field of positive characteristic. We investigate ACM, almost Ulrich (both ACM and weakly Ulrich), and Ulrich properties of the sheaves of locally exact and closed $i$-forms $B_X^i$, $Z_X^i$. These cohomological properties are closely related to the fundamental concepts of Frobenius splitting and ordinarity. Joshi studied the sheaf $B^1_X$ in this context in \\cite{MR3920911, MR4206787}, including ACM and almost Ulrich twists of $B^1_X$. However, varieties with Ulrich twisted $B_X^1$ have not been classified for $n\\ge2$. We classify subcanonical polarized varieties with initialized ACM $B^i_X(aH)$ for $i=1, n$ and prove that, for $n \\ge 2$, varieties with ACM $B^i_X$ for all $i \\le \\left\\lceil\\frac{n}{2}\\right\\rceil$ are ordinary. When $X$ is ordinary with trivial $Ω^1_X$, almost Ulrich twists of $B^i_X$ and $F_*^e(Z_X^i(aH))$ are determined. We classify polarized varieties $(X,H)$ with $B_X^i(aH)$ Ulrich when $n=1, 2$, and establish strong necessary criteria for $n \\geq 3$, together with an example. We also prove that $Z_X^i(aH)$ is never Ulrich. Finally, we classify polarized abelian varieties with Ulrich $B^1_X \\otimes L$ allowing twists by arbitrary line bundles.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28464",
  "author_total": 1,
  "authors": [
    {
      "name": "Jagadish Pine"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b9ft6hn14kyaw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28464",
  "fulltext_url": null,
  "id": "b9ft6hn14kyaw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28464",
  "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": "W7223111336",
  "pdf_url": "https://arxiv.org/pdf/2610.28464",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b9ft6hn14kyaw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.28464",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28464"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "ACM, almost Ulrich, and Ulrich vector bundles arising from Frobenius",
  "title_text": "ACM, almost Ulrich, and Ulrich vector bundles arising from Frobenius",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/b9ft6hn14kyaw",
  "venue": "arXiv",
  "versions": []
}