{"paper":{"title":"Logarithmic bundles of multi-degree arrangements in $\\mathbf{P}^{n}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Elena Angelini","submitted_at":"2014-10-31T15:23:14Z","abstract_excerpt":"Let $ \\mathcal{D} = \\{D_{1}, ..., D_{\\ell}\\} $ be a multi-degree arrangement with normal crossings on the complex projective space $ \\mathbf{P}^{n} $, with degrees $ d_{1}, ..., d_{\\ell} $; let $ \\Omega_{\\mathbf{P}^{n}}^{1}(\\log \\mathcal{D}) $ be the logarithmic bundle attached to it. First we prove a Torelli type theorem when $ \\mathcal{D} $ has a sufficiently large number of components by recovering them as unstable smooth irreducible degree-$ d_{i} $ hypersurfaces of $ \\Omega_{\\mathbf{P}^{n}}^{1}(\\log \\mathcal{D}) $. Then, when $ n = 2 $, by describing the moduli spaces containing $ \\Omega_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8770","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"}