{"paper":{"title":"$\\Lambda$-modules and holomorphic Lie algebroid connections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Pietro Tortella","submitted_at":"2011-08-16T18:16:50Z","abstract_excerpt":"Let $X$ be a complex smooth projective variety, and $\\mathcal{G}$ a locally free sheaf on $X$. We show that there is a 1-to-1 correspondence between pairs $(\\Lambda,\\Xi)$, where $\\Lambda$ is a sheaf of almost polynomial filtered algebras over $X$ satisfying Simpson's axioms and $\\Xi: \\Gr\\Lambda \\rightarrow \\Sym^\\bullet_{\\corO_X} \\mathcal{G}$ is an isomorphism, and pairs $(\\mathcal{L},\\Sigma)$, where $\\mathcal{L}$ is a holomorphic Lie algebroid structure on $\\mathcal{G}$ and $\\Sigma$ is a class in $F^1H^2(\\mathcal{L},\\C)$, the first Hodge filtration piece of the second cohomology of $\\bella$.\n "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3306","kind":"arxiv","version":3},"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"}