{"paper":{"title":"Syzygies of differentials of forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Aron Simis (Universidade Federal de Pernambuco, Brazil), Isabel Bermejo (Universidad de La Laguna, Philippe Gimenez (Universidad de Valladolid, Spain)","submitted_at":"2011-12-19T18:22:39Z","abstract_excerpt":"Given a standard graded polynomial ring $R=k[x_1,...,x_n]$ over a field $k$ of characteristic zero and a graded $k$-subalgebra $A=k[f_1,...,f_m]\\subset R$, one relates the module $\\Omega_{A/k}$ of K\\\"ahler $k$-differentials of $A$ to the transposed Jacobian module $\\mathcal{D}\\subset \\sum_{i=1}^n R dx_i$ of the forms $f_1,...,f_m$ by means of a {\\em Leibniz map} $\\Omega_{A/k}\\rar \\mathcal{D}$ whose kernel is the torsion of $\\Omega_{A/k}$. Letting $\\fp$ denote the $R$-submodule generated by the (image of the) syzygy module of $\\Omega_{A/k}$ and $\\fz$ the syzygy module of $\\mathcal{D}$, there is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4427","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"}