{
  "abstract": "Let $X$ be a log del Pezzo surface with only $\\frac13(1,1)$ singularities. We compare the derived categories of its minimal resolution, canonical stack, and singular surface. For every family in the Corti--Heuberger classification, Orlov's blow-up formula and the Ishii--Ueda correspondence give explicit full exceptional collections on the canonical stacks, of length $12-K_X^2+\\frac{4k}{3}$ when $X$ has $k$ singular points. In the one-point index-one cascade, the canonical stacks are blow-ups of the weighted projective stack $\\mathbb P(1,1,3)$ at distinct smooth points and admit explicit full strong exceptional collections of line bundles. For quasismooth hypersurfaces $X_{10}\\subset\\mathbb P(1,2,3,5)$, we construct a full strong exceptional collection of $13$ objects with an explicitly computed Euler matrix. The exceptional lattice determines the Brauer group: $\\mathrm{Br}(X)=0$ for $k\\leq5$, while $\\mathrm{Br}(X)\\cong\\mathbb Z/3$ for $k=6$. We construct semiorthogonal decompositions of $D^b(\\mathrm{coh}\\,X)$ for the one- and three-point cascades and of a Brauer-twisted derived category for the six-point cascade.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.18238",
  "author_total": 1,
  "authors": [
    {
      "name": "Alex Junior Gomez Saltachin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9tkbjsxqyx2c9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.18238",
  "fulltext_url": null,
  "id": "9tkbjsxqyx2c9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.18238",
  "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": "W7165050175",
  "pdf_url": "https://arxiv.org/pdf/2606.18238",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9tkbjsxqyx2c9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2606.18238",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.18238"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Derived categories of log del Pezzo surfaces with $\\frac13(1,1)$ singularities",
  "title_text": "Derived categories of log del Pezzo surfaces with 1/3(1,1) singularities",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/9tkbjsxqyx2c9",
  "venue": "arXiv",
  "versions": []
}