{"paper":{"title":"Plumbings of lens spaces and crepant resolutions of compound $A_n$ singularities","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.SG","authors_text":"Bilun Xie, Yin Li","submitted_at":"2025-11-28T02:02:50Z","abstract_excerpt":"For many compound $A_n$ ($cA_n$) singularities $R_f=\\mathbb{C}[u,v,x,y]/(uv-f(x,y))$ with crepant resolutions $Y_f$, their mirrors are affine $A_n$ plumbings $W^\\circ_f$ of $3$-dimensional lens spaces along circles. We prove two versions of homological mirror symmetry for these Stein $3$-folds.\n  (i) The uncompleted version: there is an equivalence $D^\\mathit{perf}\\mathcal{W}(W_f^\\circ)\\simeq D^b\\mathit{Coh}(Y^\\circ_f)$ between the derived wrapped Fukaya category and the bounded derived category of coherent sheaves on some divisor complement $Y^\\circ_f=Y_f\\setminus D$.\n  (ii) The completed ver"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.22837","kind":"arxiv","version":2},"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/2511.22837/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"}