{
  "abstract": "This paper is primarily concerned with the existence of a symplectic $4$-manifold, homeomorphic but not diffeomorphic to $CP^2$, which admits a nontrivial finite order symplectomorphism. We reduced the existence of such an exotic $CP^2$ to a question in contact geometry. More concretely, we showed that there are precisely $12$ plumbed manifolds, each equipped with a canonical contact structure associated to the plumbing, such that an exotic $CP^2$ with a nontrivial finite order symplectomorphism exists if and only if one of the $12$ contact plumbed manifolds admits a certain specific symplectic filling. As the main technical result, we completely determined the order and local representations of a pseudofree symplectic $Z_p$-action for an odd prime $p$ on a rational homology $CP^2$ with positive canonical class. Our result suggests that potentially, there are symplectic $Z_p$-actions which are not a finite automorphism of a fake projective plane. Moreover, we introduced a construction, which, under the minimal assumptions on the symplectic fillings of the $12$ contact plumbed manifolds, produces a symplectic $4$-manifold on the Bogomolov-Miyaoka-Yau line via a reverse-engineering process.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06746",
  "author_total": 1,
  "authors": [
    {
      "name": "Weimin Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a4d60yr2317p6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06746",
  "fulltext_url": null,
  "id": "a4d60yr2317p6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06746",
  "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"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "arxiv",
      "math.SG"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7220715824",
  "pdf_url": "https://arxiv.org/pdf/2610.06746",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a4d60yr2317p6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.06746",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06746"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Symplectic symmetries of a hypothetical exotic $CP^2$: a potential construction or a nonexistence proof",
  "title_text": "Symplectic symmetries of a hypothetical exotic CP^2: a potential construction or a nonexistence proof",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/a4d60yr2317p6",
  "venue": "arXiv",
  "versions": []
}