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We also prove a logarithmic version, effective in low dimension, for the log-pair $(\\mathbb P^n,D)$, where $D$ is a smooth irreducible divisor of high degree. Moreover, these result are sharp, \\emph{i.e.} one cannot have such jet differentials of order less than $n$."},"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":"0802.0045","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-02-01T12:22:29Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"9d1d50f8035a45c6d0b193eedc9d3bccc886ece3072f41e778e53efb2ec70c43","abstract_canon_sha256":"df3f2e6fdd0bf9bc64175ca4db6a25b8bd663e6007f0f7fdb127e9bc787d887f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:31.908131Z","signature_b64":"Aa/WlYP8GaL55rKaMS/AU4fVHD+yDZ8vCSUxiM76qmKbL0QpjUI33S3DysKDZMOGeI1U5aDEniJ11OFf86J/Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"37a0e2dcd716f1cb01114021b6115321ece8b598fc8dd042908c346b82f32c9d","last_reissued_at":"2026-05-18T00:47:31.907500Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:31.907500Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence of global invariant jet differentials on projective hypersurfaces of high degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Simone Diverio","submitted_at":"2008-02-01T12:22:29Z","abstract_excerpt":"Let $X\\subset\\mathbb P^{n+1}$ be a smooth complex projective hypersurface. 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