{
  "abstract": "Physical heuristics suggest that the space of Bridgeland stability conditions of a projective Calabi-Yau manifold $X$ should be related to the moduli space of complex structures on its mirror $X^\\vee$. On the other hand, recent work in the literature introduces a modular partial compactification, $\\mathcal{A}\\mathrm{Stab}(X)$, of a quotient of the space of stability conditions on $\\mathcal{D}^{b}(X)$. We provide some mathematical evidence for the aforementioned heuristics by proving that for curves and surfaces, certain boundary strata in $\\mathcal{A}\\mathrm{Stab}(X)$ describe degenerate complex structures on $X^\\vee$. Along the way, we introduce a criterion for producing boundary points of $\\mathcal{A}\\mathrm{Stab}(\\mathcal{D})$ when $\\mathcal{D}$ is an arbitrary $k$-linear triangulated category. As a byproduct, we deduce the existence of Bridgeland stability conditions on certain quotients of the derived categories of K3 and Enriques surfaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40035",
  "author_total": 2,
  "authors": [
    {
      "name": "Antonios-Alexandros Robotis"
    },
    {
      "name": "Nicolás Vilches"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e2tyjxxnvexrz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40035",
  "fulltext_url": null,
  "id": "e2tyjxxnvexrz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40035",
  "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-ph"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.SG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40035",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e2tyjxxnvexrz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:23Z",
      "native_id": "2610.40035",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40035"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.SG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Degenerate complex structures on surfaces and stability conditions",
  "title_text": "Degenerate complex structures on surfaces and stability conditions",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/e2tyjxxnvexrz",
  "venue": "arXiv",
  "versions": []
}