{
  "family_id": "039",
  "title": "Nagata’s conjecture and maximal Seshadri constants",
  "discipline": "Algebraic and complex geometry",
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  "papers": [
    {
      "title": "Nagata's conjecture for plane curves",
      "path": "preprints/Nagatas-Conjecture-for-Plane-Curves-September-23-2026/main.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Nagatas-Conjecture-for-Plane-Curves-September-23-2026/main.pdf",
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    },
    {
      "title": "Maximal Seshadri constants on arbitrary polarized surfaces",
      "path": "preprints/Maximal-Seshadri-Constants-on-Arbitrary-Polarized-Surfaces-September-23-2026/main.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Maximal-Seshadri-Constants-on-Arbitrary-Polarized-Surfaces-September-23-2026/main.pdf",
      "readme_path": "preprints/Maximal-Seshadri-Constants-on-Arbitrary-Polarized-Surfaces-September-23-2026/README.md",
      "tex_paths": [],
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    },
    {
      "title": "Maximal Multipoint Seshadri Constants in Higher Dimensions",
      "path": "preprints/Maximal-Multipoint-Seshadri-Constants-in-Higher-Dimensions-October-5-2026/main.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Maximal-Multipoint-Seshadri-Constants-in-Higher-Dimensions-October-5-2026/main.pdf",
      "readme_path": "preprints/Maximal-Multipoint-Seshadri-Constants-in-Higher-Dimensions-October-5-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    },
    {
      "title": "Maximal multipoint Seshadri constants in positive characteristic",
      "path": "preprints/Maximal-multipoint-Seshadri-constants-in-positive-characteristic-October-5-2026/seshadri-positive-characteristic.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Maximal-multipoint-Seshadri-constants-in-positive-characteristic-October-5-2026/seshadri-positive-characteristic.pdf",
      "readme_path": "preprints/Maximal-multipoint-Seshadri-constants-in-positive-characteristic-October-5-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    }
  ],
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  "lean_scope_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean/docs/039.md",
  "verification_status": "scope_document_available_not_independently_verified",
  "review_status": "inventory_complete_deep_review_pending"
}