{
  "abstract": "This paper gives a partial answer to a question of Dan Abramovich: consider a proper morphism $f : \\mathcal{X} \\to \\mathcal{Z}$ with connected fibers, between smooth separated Deligne--Mumford stacks, which defines an isomorphism away from a smooth effective Cartier divisor $\\mathcal{E} \\subseteq \\mathcal{X}$. Then, is $f$ a weighted blowup? We confirm that $f$ is an ordinary smooth blowup when $\\mathcal{X}$ and $\\mathcal{Z}$ are smooth separated schemes of finite type over $\\mathbb{C}$, and when $f :\\mathcal{X} \\to \\mathcal{Z}$ is a representable morphism of smooth separated Deligne--Mumford stacks. Further, we show that $f$ is a weighted blowup when $\\mathcal{X}$ and $\\mathcal{Z}$ are smooth separated Deligne--Mumford surfaces, i.e., $\\dim \\mathcal{X} = \\dim \\mathcal{Z} = 2$. As an application we determine when a reduction morphism between Hassett moduli stacks of weighted stable curves is given by a blowup along a smooth center.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04023",
  "author_total": 2,
  "authors": [
    {
      "name": "Soham Ghosh"
    },
    {
      "name": "Tyson Klingner"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e3cwm7vtrbm9t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04023",
  "fulltext_url": null,
  "id": "e3cwm7vtrbm9t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04023",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7208781520",
  "pdf_url": "https://arxiv.org/pdf/2609.04023",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e3cwm7vtrbm9t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.04023",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04023"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Characterizing Contractions and Weighted Blowdowns",
  "title_text": "Characterizing Contractions and Weighted Blowdowns",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/e3cwm7vtrbm9t",
  "venue": "arXiv",
  "versions": []
}