{
  "abstract": "We study differential equations -- not necessarily monic -- for Jacobi modular forms. As an application, we derive a second-order differential equation for the elliptic genus of a $K3$ surface involving the logarithmic derivative of the modular invariant $j(τ)$, and we explicitly find a third-order equation with a leading coefficient of weight 12 for the elliptic genus of any four-dimensional Calabi--Yau variety. Furthermore, we propose a simple recursive algorithm for investigating second-order differential equations with leading coefficient $E_4(τ)$ or $E_6(τ)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26768",
  "author_total": 2,
  "authors": [
    {
      "name": "Dmitrii Adler"
    },
    {
      "name": "Valery Gritsenko"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7hwqctqra36m8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26768",
  "fulltext_url": null,
  "id": "7hwqctqra36m8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26768",
  "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",
      "2602|Advanced Mathematical Identities"
    ]
  ],
  "openalex": "W7223000583",
  "pdf_url": "https://arxiv.org/pdf/2610.26768",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7hwqctqra36m8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:31:00Z",
      "native_id": "2610.26768",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26768"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Meromorphic modular differential equations for the elliptic genus of Calabi--Yau varieties",
  "title_text": "Meromorphic modular differential equations for the elliptic genus of Calabi--Yau varieties",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:47Z",
  "url": "https://research.draconitic.com/paper/7hwqctqra36m8",
  "venue": "arXiv",
  "versions": []
}