{
  "abstract": "A Lagrangian submanifold in an almost Calabi-Yau manifold is called positive if the real part of the holomorphic volume form restricted to it is positive. It is called $ε$-positive if the ratio of the restrictions of the imaginary and real parts of the holomorphic volume form is bounded by $\\frac{1}ε.$ An exact isotopy class of positive Lagrangian submanifolds admits a natural Riemannian metric. We prove that the Riemannian metric restricted to the subset of $ε$-positive Lagrangians induces a path metric when the relative Kähler class of the ambient Calabi-Yau manifold lies on a line of rational slope. The proof relies on the construction of a sequence of quantization maps from a circle bundle over the space of positive Lagrangians to the dual of the space of holomorphic sections of powers of a prequantum line bundle. The rationality condition for the relative Kähler class allows us to reduce to the case of Bohr-Sommerfeld Lagrangians. Building on ideas of Tian and Nirenberg-Wells, Hörmander estimates are used to show that functions on a Bohr-Sommerfeld Lagrangian can be approximated by holomorphic sections of a sufficiently high power of the prequantum line bundle. Consequently, the quantization maps eventually separate fibers of the circle bundle.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20177",
  "author_total": 2,
  "authors": [
    {
      "name": "Jake P. Solomon"
    },
    {
      "name": "Bentzion Yavetz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2cs8rbre66gtz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20177",
  "fulltext_url": null,
  "id": "2cs8rbre66gtz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20177",
  "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",
      "hep-th"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "arxiv",
      "math.SG"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7221893402",
  "pdf_url": "https://arxiv.org/pdf/2610.20177",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2cs8rbre66gtz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:31Z",
      "native_id": "2610.20177",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20177"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Quantization of positive Lagrangians",
  "title_text": "Quantization of positive Lagrangians",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/2cs8rbre66gtz",
  "venue": "arXiv",
  "versions": []
}