{"paper":{"title":"L^2-Betti numbers of hypersurface complements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AT","authors_text":"Laurentiu Maxim","submitted_at":"2012-02-03T23:44:43Z","abstract_excerpt":"In \\cite{DJL07} it was shown that if $\\scra$ is an affine hyperplane arrangement in $\\C^n$, then at most one of the $L^2$--Betti numbers $b_i^{(2)}(\\C^n\\sm \\scra,\\id)$ is non--zero. In this note we prove an analogous statement for complements of complex affine hyperurfaces in general position at infinity. Furthermore, we recast and extend to this higher-dimensional setting results of \\cite{FLM,LM06} about $L^2$--Betti numbers of plane curve complements."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.0844","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"}