{
  "abstract": "Let $D$ be a smooth divisor in a smooth projective complex variety $X$. For connected curves of arithmetic genus one with prescribed signed contact orders, we prove that the refined punctured cycle of Battistella--Nabijou--Ranganathan and the negative-contact cycle of Fan--Wu--You agree after pushforward to the common moduli space of stable maps with divisor evaluations. Thus the pushed-forward refined punctured cycle is the constant coefficient of the pushed-forward root-stack virtual class, normalized by one power of the root order for each negative contact. The key step is a comparison for the universal target. After restricting to finite-type open substacks determined by the fixed pair $(X,D)$ and numerical data $Γ$, we prove that the positive BNR space maps finitely and with generic degree one onto Crumplin's main component. Using Crumplin's genus-one component description and degree formulas, we identify this component's fundamental cycle with the constant coefficient of the universal orbifold virtual class under comparison of root orders. Refined zero-section pullback recovers the negative contacts, and compatible virtual pullbacks and root-forgetting pushforwards transfer the resulting identity to $(X,D)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08124",
  "author_total": 1,
  "authors": [
    {
      "name": "Yu Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a5r9tpk3yp7py.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08124",
  "fulltext_url": null,
  "id": "a5r9tpk3yp7py",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08124",
  "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-ph"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7212038019",
  "pdf_url": "https://arxiv.org/pdf/2609.08124",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a5r9tpk3yp7py.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:49Z",
      "native_id": "2609.08124",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08124"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Negative contacts in genus one: a comparison of punctured and root stack Gromov-Witten theories",
  "title_text": "Negative contacts in genus one: a comparison of punctured and root stack Gromov-Witten theories",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/a5r9tpk3yp7py",
  "venue": "arXiv",
  "versions": []
}