{"paper":{"title":"Sobolev spaces and Bochner Laplacian on complex projective varieties and stratified pseudomanifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Francesco Bei","submitted_at":"2015-05-03T15:13:19Z","abstract_excerpt":"Let $V\\subset \\mathbb{C}\\mathbb{P}^n$ be an irreducible complex projective variety of complex dimension $v$ and let $g$ be the K\\\"ahler metric on $\\reg(V)$, the regular part of $V$, induced by the Fubini Study metric of $\\mathbb{C}\\mathbb{P}^n$. In this setting Li and Tian proved that $W^{1,2}_0(\\reg(V),g)=W^{1,2}(\\reg(V),g)$, that the natural inclusion $W^{1,2}(\\reg(V),g)\\hookrightarrow L^2(\\reg(V),g)$ is a compact operator and that the heat operator associated to the Friedrich extension of the scalar Laplacian $\\Delta_0:C^{\\infty}_c(\\reg(V))\\rightarrow C^{\\infty}_c(\\reg(V))$, that is $e^{-t\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00439","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"}