{"paper":{"title":"Hilbert Schemes of Points in the Plane and Quasi-Lisse Vertex Algebras with $\\mathcal{N}=4$ Symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.AG","math.QA"],"primary_cat":"math.RT","authors_text":"Sven M\\\"oller, Tomoyuki Arakawa, Toshiro Kuwabara","submitted_at":"2023-09-29T15:05:58Z","abstract_excerpt":"To each complex reflection group $\\Gamma$ one can attach a canonical symplectic singularity $\\mathcal{M}_\\Gamma$ arXiv:math/9903070. Motivated by the 4D/2D duality arXiv:1312.5344, arXiv:1707.07679, Bonetti, Meneghelli and Rastelli arXiv:1810.03612 conjectured the existence of a supersymmetric vertex operator superalgebra $\\mathsf{W}_\\Gamma$ whose associated variety is isomorphic to $\\mathcal{M}_\\Gamma$. We prove this conjecture when the complex reflection group $\\Gamma$ is the symmetric group $S_N$ by constructing a sheaf of $\\hbar$-adic vertex operator superalgebras on the Hilbert scheme of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.17308","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/2309.17308/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"}