{"paper":{"title":"Differentials of Cox rings: Jaczewski's theorem revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jaroslaw A. Wisniewski, Oskar Kedzierski","submitted_at":"2011-04-04T20:34:29Z","abstract_excerpt":"A generalized Euler sequence over a complete normal variety X is the unique extension of the trivial bundle V \\otimes O_X by the sheaf of differentials \\Omega_X, given by the inclusion of a linear space V in Ext^1(O_X,\\Omega_X). For \\Lambda, a lattice of Cartier divisors, let R_\\Lambda denote the corresponding sheaf associated to V spanned by the first Chern classes of divisors in \\Lambda. We prove that any projective, smooth variety on which the bundle R_\\Lambda splits into a direct sum of line bundles is toric. We describe the bundle R_\\Lambda in terms of the sheaf of differentials on the ch"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0685","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"}