{"paper":{"title":"Mirror functor for deformed preprojective algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.SG","authors_text":"Hansol Hong, Ju Tan, Siu-Cheong Lau","submitted_at":"2026-08-06T08:52:01Z","abstract_excerpt":"We study localized homological mirror symmetry associated to an immersed Lagrangian brane $\\mathbb{L}$, possibly equipped with a higher rank flat bundle, of a symplectic manifold $X$. Under a certain finiteness assumption on the Floer theory of $\\mathbb{L}$, we deduce a quasi-equivalence $\\mathcal{D}\\mathrm{Fuk}_\\mathbb{L}(X) \\cong \\mathcal{D}_{\\mathrm{fd}}(\\tilde{\\mathcal A}_\\mathbb{L})$ using Koszul duality, where $\\tilde{\\mathcal{A}}_{\\mathbb{L}}$ is the dual differential graded quiver algebra called the extended localized mirror. We apply this to obtain some HMS results for plumbings of co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.05764","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/2608.05764/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"}