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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} "},"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":"1506.01931","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-06-05T14:54:53Z","cross_cats_sorted":[],"title_canon_sha256":"4d38e859845f67d0397f0d71e7191c15c77a7ad45dfa53846a8db3029c08fd1b","abstract_canon_sha256":"56672b39482a19926348b348735bd5c27769a61adcad16c197c0a11371a4ac58"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:55:58.892926Z","signature_b64":"yWSdCBPqf9AgECShtWuigS3ZS0yAgq6HjVDx6d10QtWN5NnttmXzKKydyoVPHzsznqffGVGRLOMEMUP1E6mKAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1fa3054327099027662ee9e51aa31c00bb7615da60e26d5f660bf0f7383c2dd1","last_reissued_at":"2026-05-18T01:55:58.892364Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:55:58.892364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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}) $. 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