{"paper":{"title":"The Weight Filtration on the Constant Sheaf on a Parameterized Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Brian Hepler","submitted_at":"2018-11-11T00:24:23Z","abstract_excerpt":"On an $n$-dimensional locally reduced complex analytic space $X$ on which the shifted constant sheaf $\\Q_X^\\bullet[n]$ is perverse, it is well-known that, locally, $\\Q_X^\\bullet[n]$ underlies a mixed Hodge module of weight $\\leq n$ on $X$, with weight $n$ graded piece isomorphic to the intersection cohomology complex $\\Idot_X$ with constant $\\Q$ coefficients. In this paper, we identify the weight $n-1$ graded piece $\\Gr_{n-1}^W \\Q_X^\\bullet[n]$ in the case where $X$ is a \"parameterized space\", using the comparison complex, a perverse sheaf naturally defined on any space for which the shifted c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.04328","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":""},"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"}