{"paper":{"title":"The LLV Algebra for Primitive Symplectic Varieties with Isolated Singularities","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Benjamin Tighe","submitted_at":"2022-11-13T01:05:15Z","abstract_excerpt":"We extend results of Looijenga--Lunts and Verbitsky and show that the total Lie algebra $\\mathfrak g$ for the intersection cohomology of a primitive symplectic variety $X$ with isolated singularities is isomorphic to $$\\mathfrak g \\cong \\mathfrak{so}\\left(\\left(IH^2(X, \\mathbb Q), Q_X\\right)\\oplus \\mathfrak h\\right),$$ where $Q_X$ is the intersection Beauville--Bogomolov--Fujiki form and $\\mathfrak h$ is a hyperbolic plane. This gives a new, algebraic proof for irreducible holomorphic symplectic manifolds which does not rely on the hyperk\\\"ahler metric.\n  Along the way, we study the structure "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.06776","kind":"arxiv","version":4},"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/2211.06776/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"}