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This is a classical way to construct and study projective schemes (e.g. see \\cite{hart-1974}, \\cite{hart-2}, \\cite{mdp}, \\cite{serre-1960}). In particular, we give homological conditions on $ \\mathcal P $ and $ \\mathcal N $ that force $ D $ to be ACM, without constrains on its codimension. As last result, we prove that if $ \\mathcal N $ is a higher syzygy sheaf of an ACM scheme $ X,$ the scheme $ D $ we get"},"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":"1202.3551","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-02-16T10:04:45Z","cross_cats_sorted":[],"title_canon_sha256":"81c5a90b2b498077f2aba8e08b8204795d4470867189b499f9cfca4f25298d5c","abstract_canon_sha256":"affd1ff629a12839d76ffc651ebbbfc24120b3de13a79a7fff73f12db69955ff"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:12.898902Z","signature_b64":"/cQrDNfEXMoSsITg1GylbYp+zUBqd8RzbWbceYME5zDxy7Hxdq2JRUOM1yZ6sQGaL9AnYfjYN1RYbbeQD/ZMDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"454aeceb615453c562b86decf9f0458f0933df41a5a4f5ee31637156c2e1a40c","last_reissued_at":"2026-05-18T04:02:12.898218Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:12.898218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Torsion-free Sheaves and ACM Schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"M.L. 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