{"paper":{"title":"The Holomorphic Extension Property for Higher Du Bois Singularities","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Benjamin Tighe","submitted_at":"2023-12-02T23:07:12Z","abstract_excerpt":"Let $X$ be a normal complex variety and $\\pi:\\tilde X \\to X$ a resolution of singularities. We show that the inclusion morphism $\\pi_*\\Omega_{\\tilde X}^p\\hookrightarrow \\Omega_X^{[p]}$ is an isomorphism for $p < \\mathrm{codim}_X(X_{\\mathrm{sing}})$ when $X$ has du Bois singularities, giving an improvement on Flenner's criterion for arbitrary singularities. We also study the $k$-du Bois definition from the perspective of holomorphic extension and compare how different restrictions on $\\mathscr H^0(\\underline \\Omega_X^p)$ affect the singularities of $X$, where $\\underline\\Omega_X^p$ is the $p^{t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.01245","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2312.01245/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"}