{
  "id": "2208.14485",
  "version": "v1",
  "published": "2022-08-30T18:23:45.000Z",
  "updated": "2022-08-30T18:23:45.000Z",
  "title": "Recent progress on SYZ mirror symmetry for some non-compact Calabi-Yau surfaces",
  "authors": [
    "Tristan C. Collins",
    "Yu-Shen Lin"
  ],
  "comment": "survey article; 29 pages",
  "categories": [
    "math.DG",
    "math.AG"
  ],
  "abstract": "We survey the authors recent works, joint with A. Jacob, on Strominger-Yau-Zaslow mirror symmetry for rational elliptic surfaces and del Pezzo surfaces. We discuss some applications, including the Torelli theorem for $ALH^*$ gravitational instantons and explain how our results can be used to prove that all $ALH^*$ gravitational instantons can be compactified to a weak del Pezzo surface, recovering a recent result of Hein-Sun-Viaclovsky-Zhang.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-30T18:23:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "syz mirror symmetry",
      "non-compact calabi-yau surfaces",
      "weak del pezzo surface",
      "gravitational instantons",
      "strominger-yau-zaslow mirror symmetry"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}