{
  "abstract": "We study the half weight ($N=\\half$) analogue of the Bers quasiform on a Schottky group $Γ$ of genus $g$: the Poincaré series $S_\\eps(x,y)=\\sum_{\\gt\\in\\Gt}j(\\gt,x)/(γx-y)\\,(dx\\,dy)^{1/2}$ over a lift $\\Gt\\subset\\mathrm{SL}_2(\\C)$ of $Γ$. The $\\Ng:=2^{g}$ lifts give $\\Ng$ trivial $α$-holonomy even spin structures $\\Lg$. The remaining $2^{2g}-\\Ng$ spin structures are not treated in this paper. We prove, on an open set (H) of Schottky parameters and more generally whenever the critical exponent of $Γ$ is below $\\half$ (any genus $g\\ge 1$) the following: absolute and locally uniform convergence on $Ω_0\\timesΩ_0$, where $Ω_0$ is the full region of discontinuity including the point $\\infty$ (treated in homogeneous coordinates); invariance without Eichler-type defect; skew-symmetry; a simple pole on the diagonal as the only singularity; $H^0(\\Sg,\\Lg)=0$; and hence identification of $S_\\eps$ with the Szegő kernel of $\\Lg$. At genus one the kernel is computed explicitly and the relations between lifts and theta characteristics are determined. We further prove that the diagonal coefficient defines a projective connection that differs from the Bergman projective connection by a quadratic differential constructed from $θ[δ](0)$, a residue-reconstruction formula for half-differentials with poles of any order, an expansion in the Schottky multipliers, and a formula for the free fermion stress tensor.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06446",
  "author_total": 1,
  "authors": [
    {
      "name": "A. Zuevsky"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3ece3vd03damp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06446",
  "fulltext_url": null,
  "id": "3ece3vd03damp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06446",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06446",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3ece3vd03damp.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06446",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06446"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Szegő quasiforms: a Schottky-scheme construction for vertex operator superalgebras",
  "title_text": "Szegő quasiforms: a Schottky-scheme construction for vertex operator superalgebras",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:30Z",
  "url": "https://research.draconitic.com/paper/3ece3vd03damp",
  "venue": "arXiv",
  "versions": []
}