{"paper":{"title":"Hessenberg varieties and hyperplane arrangements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CO","math.RT","math.SG"],"primary_cat":"math.AG","authors_text":"Mikiya Masuda, Satoshi Murai, Takashi Sato, Takuro Abe, Tatsuya Horiguchi","submitted_at":"2016-11-01T15:22:00Z","abstract_excerpt":"Given a semisimple complex linear algebraic group $G$ and a lower ideal $I$ in positive roots of $G$, three objects arise: the ideal arrangement $\\mathcal{A}_I$, the regular nilpotent Hessenberg variety $\\mbox{Hess}(N,I)$, and the regular semisimple Hessenberg variety $\\mbox{Hess}(S,I)$. We show that a certain graded ring derived from the logarithmic derivation module of $\\mathcal{A}_I$ is isomorphic to $H^*(\\mbox{Hess}(N,I))$ and $H^*(\\mbox{Hess}(S,I))^W$, the invariants in $H^*(\\mbox{Hess}(S,I))$ under an action of the Weyl group $W$ of $G$. This isomorphism is shown for general Lie type, an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.00269","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":""},"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"}