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We study the relationships between the Betti numbers of the module H^0_*(E) and the integers, d; \\tau, where \\tau = deg(\\Sigma). We observe that our results apply to any quasi-complete intersection of type (s; s; s)."},"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":"1902.05472","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-02-14T16:10:22Z","cross_cats_sorted":[],"title_canon_sha256":"83ca4ee6c5fde05f60cc2df9bebbfcc4ec67bd67d5b7a4dc2f0faab0d4db1c9e","abstract_canon_sha256":"45c540638a09cdde4bfd66f1e53efea988a2d2a0671459c1d02f1b2f32935bb5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:41.731112Z","signature_b64":"TkW6mxszDyDZ8y42i/+RV0wNGpArWWCFcPl78tjlp+i/PJLpzxZ1We9efW1Fbl+/J6DXl5poas5arLvGWJsbDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d42ecbd809212336eb851fa20d66f34e033255c520ce71e59beeaafe3dd37bf","last_reissued_at":"2026-05-17T23:51:41.730702Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:41.730702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quasi-complete intersections in P2 and syzygies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Philippe Ellia","submitted_at":"2019-02-14T16:10:22Z","abstract_excerpt":"Let C \\in P2 be a reduced, singular curve of degree d and equation f = 0. 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