{
  "abstract": "Let $X$ be a normal variety in arbitrary characteristic, and let $\\tilde X$ be the successive blowup along subvarieties $Z_1,\\dotsc,Z_n\\subseteq X$ of codimension at least two that have simple normal crossings and satisfy $Z_h\\not\\supseteq Z_i$ whenever $h<i$. We prove that the relative cone of curves $\\overline{\\operatorname{NE}}(\\tilde X/X)$ is generated by the classes of finitely many elementary curves, and that every face admits a contraction over $X$. Moreover, we prove that every small face contraction admits a $D$-flip for every $\\mathbb R$-Cartier divisor $D$ that is relatively anti-ample. We also compute the relative Cox sheaf and prove its finite generation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18936",
  "author_total": 1,
  "authors": [
    {
      "name": "Yuto Masamura"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8rkk3eb1er3kk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18936",
  "fulltext_url": null,
  "id": "8rkk3eb1er3kk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18936",
  "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": "W7213530891",
  "pdf_url": "https://arxiv.org/pdf/2609.18936",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8rkk3eb1er3kk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2609.18936",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18936"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Relative cone of curves and contractions of a successive blowup",
  "title_text": "Relative cone of curves and contractions of a successive blowup",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/8rkk3eb1er3kk",
  "venue": "arXiv",
  "versions": []
}