{
  "abstract": "We study the moduli space of constant scalar curvature Kähler (cscK) surfaces around toric surfaces. To this end, we introduce the class of foldable surfaces: smooth toric surfaces whose lattice automorphism group contains a non-trivial cyclic subgroup. We classify such surfaces and show that they all admit a cscK metric. We then study the moduli space of polarised cscK surfaces around a point given by a foldable surface, and show that it is locally modelled on a finite quotient of a toric affine variety with terminal singularities.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Carl Tipler"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4b7hnsavfb1wk.bib",
  "cited_by": 0,
  "doi": "10.1112/mod.2025.10005",
  "fulltext_url": null,
  "id": "4b7hnsavfb1wk",
  "issns": [
    "2949-7647"
  ],
  "landing_url": "https://hal.science/hal-05738402v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W4414520039",
  "pdf_url": "https://hal.science/hal-05738402/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4b7hnsavfb1wk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:27Z",
      "native_id": "hal-05738402",
      "source": "hal",
      "url": "https://hal.science/hal-05738402v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2608|Geometry and complex manifolds",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Foldable fans, cscK surfaces and local K-moduli",
  "title_text": "Foldable fans, cscK surfaces and local K-moduli",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:17:27Z",
  "url": "https://research.draconitic.com/paper/4b7hnsavfb1wk",
  "venue": "Moduli",
  "versions": []
}