{"paper":{"title":"On the local cohomology of secant varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Debaditya Raychaudhury, Sebastian Olano","submitted_at":"2024-07-23T17:51:52Z","abstract_excerpt":"Given a sufficiently positive embedding $X\\subset\\mathbb{P}^N$ of a smooth projective variety $X$, we consider its secant variety $\\Sigma$ that comes equipped with the embedding $\\Sigma\\subset\\mathbb{P}^N$ by its construction. In this article, we determine the local cohomological dimension $\\textrm{lcd}(\\mathbb{P}^N,\\Sigma)$ of this embedding, as well as the generation level of the Hodge filtration on the topmost non-vanishing local cohomology module $\\mathcal{H}^{q}_{\\Sigma}(\\mathcal{O}_{\\mathbb{P}^N})$, i.e., when $q=\\textrm{lcd}(\\mathbb{P}^N,\\Sigma)$. Additionally, we show that $\\Sigma$ has"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.16688","kind":"arxiv","version":1},"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/2407.16688/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"}