{
  "abstract": "We compare motivic nearby cycles at infinity with classes computed directly on rational compactifications. Let $f$ be a regular function on a smooth variety over a field of characteristic zero, and let $X$ be a smooth proper compactification. Suppose that a reduced divisor containing the boundary and the support of $\\operatorname{div}_X(f)$ has simple normal crossings near the polar locus. We prove that the open-pair class defined by $1/f$ agrees with Raibaut's compactification-independent motivic nearby cycle at infinity. The key step is a local cancellation under blow-ups of transverse zero-pole intersections. For Laurent polynomials nondegenerate at infinity, this comparison yields a direct toric proof of Raibaut's essential-face formula. Equivariant Hodge realization and weighted Ehrhart theory give Newton formulas retaining cohomological degree and the limit-weight filtration, and determine irregular Hodge numbers through the limiting-irregular comparison. The weight-forgetting specialization computes the zero-potential stringy invariant of toric stacky fans with the same radial support, yielding a motivic-Hodge derivation of the corresponding Fano-Landau-Ginzburg mirror identity. In the full-dimensional weak Fano case, the refined formulas identify monodromy eigenvalues and Jordan-block sizes with inertia ages and anticanonical Lefschetz strings, giving a noncanonical comparison over $\\mathbb C$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00289",
  "author_total": 1,
  "authors": [
    {
      "name": "Haoxu Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/68ef80tbf6kzr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00289",
  "fulltext_url": null,
  "id": "68ef80tbf6kzr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00289",
  "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",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7215708256",
  "pdf_url": "https://arxiv.org/pdf/2610.00289",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/68ef80tbf6kzr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.00289",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00289"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Motivic Vanishing Cycles at Infinity and Toric Landau-Ginzburg Mirror Symmetry",
  "title_text": "Motivic Vanishing Cycles at Infinity and Toric Landau-Ginzburg Mirror Symmetry",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/68ef80tbf6kzr",
  "venue": "arXiv",
  "versions": []
}