{"paper":{"title":"On the normal sheaf of determinantal varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Jan O. Kleppe, Rosa M. Mir\\'o-Roig","submitted_at":"2014-03-28T14:10:38Z","abstract_excerpt":"Let X be a standard determinantal scheme X \\subset \\PP^n of codimension c, i.e. a scheme defined by the maximal minors of a t \\times (t+c-1) homogeneous polynomial matrix A. In this paper, we study the main features of its normal sheaf \\shN_X. We prove that under some mild restrictions: (1) there exists a line bundle \\shL on X \\setminus Sing(X) such that \\shN_X \\otimes \\shL is arithmetically Cohen-Macaulay and, even more, it is Ulrich whenever the entries of A are linear forms, (2) \\shN_X is simple (hence, indecomposable) and, finally, (3) \\shN_X is \\mu-(semi)stable provided the entries of A a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7383","kind":"arxiv","version":3},"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"}