{"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. Spreafico, R. Notari, S. Greco","submitted_at":"2012-02-16T10:04:45Z","abstract_excerpt":"In this paper we study short exact sequences $ 0 \\to \\mathcal P \\to \\mathcal N \\to \\ii_D(k) \\to 0 $ with $ \\mathcal P, \\mathcal N $ torsion--free sheaves and $ D $ closed projective scheme. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3551","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}