{"paper":{"title":"Generalized Serre conditions and perverse coherent sheaves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Christopher L. Bremer, Daniel S. Sage","submitted_at":"2011-06-14T06:04:34Z","abstract_excerpt":"In algebraic geometry, one often encounters the following problem: given a scheme X, find a proper birational morphism from Y to X where the geometry of Y is \"nicer\" than that of X. One version of this problem, first studied by Faltings, requires Y to be Cohen-Macaulay; in this case Y is called a Macaulayfication of X. In another variant, one requires Y to satisfy the Serre condition S_r. In this paper, the authors introduce generalized Serre conditions--these are local cohomology conditions which include S_r and the Cohen-Macaulay condition as special cases. To any generalized Serre condition"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.2616","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"}