{"paper":{"title":"The Torelli problem for Logarithmic bundles of hypersurface arrangements in the projective space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Elena Angelini","submitted_at":"2015-06-05T14:54:53Z","abstract_excerpt":"Let $ \\mathcal{D} = \\{D_{1}, \\ldots, D_{\\ell}\\} $ be an arrangement of smooth hypersurfaces with normal crossings on the complex projective space $ \\mathbb{P}^{n} $ and let $ \\Omega^{1}_{\\mathbb{P}^{n}}(log \\mathcal{D}) $ be the logarithmic bundle attached to it. Our aim is to study the injectivity of the correspondence $ \\mathcal{D} \\longrightarrow \\Omega^{1}_{\\mathbb{P}^{n}}(log \\mathcal{D}) $. In order to do that, we first show that $ \\Omega^{1}_{\\mathbb{P}^{n}}(log \\mathcal{D}) $ admits a resolution of length $ 1 $ depending on the degrees and on the equations of $ D_{1}, \\ldots, D_{\\ell} "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01931","kind":"arxiv","version":1},"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"}