{"paper":{"title":"Global Koppelman formulas on (singular) projective varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Mats Andersson","submitted_at":"2017-03-27T14:12:23Z","abstract_excerpt":"Let $i\\colon X\\to \\Pk^N$ be a projective manifold of dimension $n$ embedded in projective space $\\Pk^N$, and let $L$ be the pull-back to $X$ of the line bundle $\\Ok_{\\Pk^N}(1)$. We construct global explicit Koppelman formulas on $X$ for smooth $(0,*)$-forms with values in $L^s$ for any $s$. %The formulas are intrinsic on $X$. The same construction works for singular, even non-reduced, $X$ of pure dimension, if the sheaves of smooth forms are replaced by suitable sheaves $\\A_X^*$ of $(0,*)$-currents with mild singularities at $X_{sing}$. In particular, if $s\\ge \\reg X -1$, where $\\reg X$ is the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.09091","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"}