{"paper":{"title":"Planes of matrices of constant rank and globally generated vector bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ada Boralevi, Emilia Mezzetti","submitted_at":"2014-02-10T14:43:06Z","abstract_excerpt":"We consider the problem of determining all pairs (c_1, c_2) of Chern classes of rank 2 bundles that are cokernel of a skew-symmetric matrix of linear forms in 3 variables, having constant rank 2c_1 and size 2c_1+2. We completely solve the problem in the \"stable\" range, i.e. for pairs with c_1^2-4c_2<0, proving that the additional condition c_2\\le {{c_1+1}\\choose 2} is necessary and sufficient. For c_1^2-4c_2\\ge 0, we prove that there exist globally generated bundles, some even defining an embedding of P^2 in a Grassmannian, that cannot correspond to a matrix of the above type. This extends pre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2167","kind":"arxiv","version":2},"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"}