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Ballico","submitted_at":"2014-04-24T08:55:50Z","abstract_excerpt":"Let $C\\subset \\mathbb {P}^n$ be a smooth curve and $N_C$ its normal bundle. $N_C$ satisfies strong interpolation if for all integers $s>0$ and $\\lambda _i\\in \\{0,1,\\dots ,n-1\\}$, $1\\le i \\le s$, there are distinct points $P_1,\\dots ,P_s\\in C$ and linear subspaces $U_i\\subseteq E|P_i$ such that $\\dim (U_i)= \\lambda _i$ for all $i$ and the evaluation map $H^0(E)\\to \\oplus _{i=1}^{s} U_i$ has maximal rank (A. Atanasios). We prove that $C$ satisfies strong interpolation if either $C$ is a linearly normal elliptic curve or $C$ is a general embedding of degree $d\\ge (5n-8)g+2n^2-5n+4$ of a smooth cu"},"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":"1404.6056","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-04-24T08:55:50Z","cross_cats_sorted":[],"title_canon_sha256":"d0a66baed17704a28fc05a18602525e9a0f3abb9a2b0ede7a2aa8ee0efc04faa","abstract_canon_sha256":"e6042957059d544b081b4baba793ab5393409a572df6e74409570a79a04ef229"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:53:18.509076Z","signature_b64":"yF3Wepyo0GjpNoIvj+17h4vYwAmneOxpwTNjBXz1E6Lyh8QnkgE7ic4r024Bf8Sjv1KPuh54+YcFz7ZsvSvgAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4d538b507150b4ae5e3925a5c78689432abd25b8d0124a7561cfdfc2084e29a5","last_reissued_at":"2026-05-18T02:53:18.508359Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:53:18.508359Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An interpolation problem for the normal bundle of curves of genus $g\\ge 2$ and high degree in $\\mathbb {P}^r$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"E. Ballico","submitted_at":"2014-04-24T08:55:50Z","abstract_excerpt":"Let $C\\subset \\mathbb {P}^n$ be a smooth curve and $N_C$ its normal bundle. $N_C$ satisfies strong interpolation if for all integers $s>0$ and $\\lambda _i\\in \\{0,1,\\dots ,n-1\\}$, $1\\le i \\le s$, there are distinct points $P_1,\\dots ,P_s\\in C$ and linear subspaces $U_i\\subseteq E|P_i$ such that $\\dim (U_i)= \\lambda _i$ for all $i$ and the evaluation map $H^0(E)\\to \\oplus _{i=1}^{s} U_i$ has maximal rank (A. Atanasios). 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