{"paper":{"title":"Homological mirror symmetry for projective K3 surfaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.SG","authors_text":"Ailsa Keating, Paul Hacking","submitted_at":"2025-03-07T18:40:16Z","abstract_excerpt":"We prove the homological mirror symmetry conjecture of Kontsevich for K3 surfaces in the following form: The Fukaya category of a projective K3 surface is equivalent to the derived category of coherent sheaves on the mirror, which is a K3 surface of Picard rank $19$ over the field $\\mathbb{C}((q))$ of formal Laurent series. This builds on prior work of Seidel, who proved the theorem in the case of the quartic surface, Sheridan, Lekili--Ueda, and Ganatra--Pardon--Shende."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.05680","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.05680/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}