{
  "abstract": "Let $p>3$ be a prime number. If $A$ and $B$ are two principally polarized superspecial abelian surfaces over $\\mathbb{F}_{p^{2}}$ with $p^{2}$-Frobenius $[-p]$, we prove that there exists a separable polarized isogeny between them with multiplier at most $p/\\sqrt{2}$. The multiplier bound is uniform in the pair and asymptotically optimal up to a small multiplicative constant. Given quaternionic coordinates, we provide a deterministic algorithm that satisfies this upper bound in polynomial time. For unrestricted multipliers, $\\mathrm{KLPT}^{2}$ provides a heuristic algorithm with a multiplier upper bound of order $p^{6+o(1)}$ for arbitrary pairs and $p^{3+o(1)}$ when one polarization matrix is the identity matrix. Our algorithm's improvement is an explicit upper bound below $p$ with an unconditional deterministic guarantee.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12080",
  "author_total": 1,
  "authors": [
    {
      "name": "Lam L. Pham"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4ysf5gn31vs9p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12080",
  "fulltext_url": null,
  "id": "4ysf5gn31vs9p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12080",
  "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"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7221109080",
  "pdf_url": "https://arxiv.org/pdf/2610.12080",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4ysf5gn31vs9p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.12080",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12080"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A uniform bound for the minimal degree of an isogeny between principally polarized superspecial abelian surfaces",
  "title_text": "A uniform bound for the minimal degree of an isogeny between principally polarized superspecial abelian surfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/4ysf5gn31vs9p",
  "venue": "arXiv",
  "versions": []
}