{"paper":{"title":"An alternating matrix and a vector, with application to Aluffi algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Andrew R. Kustin","submitted_at":"2015-12-27T22:56:59Z","abstract_excerpt":"Let $\\mathbf X$ be a generic alternating matrix, $\\mathbf t$ be a generic row vector, and $J$ be the ideal $\\operatorname{Pf}_4({\\mathbf X})+I_1({\\mathbf {t X}})$. We prove that $J$ is a perfect Gorenstein ideal of grade equal to the grade of $\\operatorname{Pf}_4({\\mathbf X})$ plus two. This result is used by Ramos and Simis in their calculation of the Aluffi algebra of the module of derivations of the homogeneous coordinate ring of a smooth projective hypersurface. We also prove that $J$ defines a domain, or a normal ring, or a unique factorization domain if and only if the base ring has the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08287","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"}