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We prove that if the Albanese map of $X$ is of degree $1$ onto its image then the fibers of $\\pi\\colon\\mathcal{X}\\to B$ are birational under the assumption that all the $1$-forms and all the $n$-forms of a fiber are holomorphically liftable to $\\mathcal{X}$. Moreover we show that generic Torelli ho"},"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":"1409.1826","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-05T14:50:13Z","cross_cats_sorted":[],"title_canon_sha256":"a34b3ab769dffc1f48ebc86149b6e17ae76e0b315b269f76a52732d39feb6a15","abstract_canon_sha256":"b37c881a91f6e18e592786eff2401b24cc8705c5b4fc98221473fbf7f385a9d0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:59.394569Z","signature_b64":"tCOCgrKiY2+g0OtlpcTiHqz5YXXwx/ZFKfnxQc8ITl3wMlYhfLmiM2fkFgpI3lYnuqhRUuyK7BZlxEBrstewAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"41aae1ed5ab14df23d730086d8ba0a209c8d7610643c86d7d1342c77132114b2","last_reissued_at":"2026-05-18T01:20:59.393963Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:59.393963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Differential forms and quadrics of the canonical image","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Francesco Zucconi, Luca Rizzi","submitted_at":"2014-09-05T14:50:13Z","abstract_excerpt":"Let $\\pi\\colon\\mathcal{X}\\to B$ be a family over a smooth connected analytic variety $B$, not necessarily compact, whose general fiber $X$ is smooth of dimension $n$, with irregularity $\\geq n+1$ and such that the image of the canonical map of $X$ is not contained in any quadric of rank $\\leq 2n+3$. We prove that if the Albanese map of $X$ is of degree $1$ onto its image then the fibers of $\\pi\\colon\\mathcal{X}\\to B$ are birational under the assumption that all the $1$-forms and all the $n$-forms of a fiber are holomorphically liftable to $\\mathcal{X}$. 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