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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_"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1410.8770","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-10-31T15:23:14Z","cross_cats_sorted":[],"title_canon_sha256":"2ddccbfea5fad4fb4075d0c72370fb50ab163b29967373c8494b11121b05a891","abstract_canon_sha256":"53c5ba394e9e1b7a4c78ca3eb57f38bc2456d42b61cce63d4ae7d06121aab227"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:55:59.863391Z","signature_b64":"uRytK9IyA3HqQ4oPjxT7hZc8LczqAvBNnSG2gT1WxOVpNBXfNTzaG+t26R4pJDCml/P/IKTCwHxG3R9Mld8sDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d587b7b661898266f6b53e94c5d48b7984b4a3059409f5c5eb140db9a827878","last_reissued_at":"2026-05-18T01:55:59.863013Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:55:59.863013Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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}) $. 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