{"paper":{"title":"On higher Hessians and the Lefschetz properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Rodrigo Gondim","submitted_at":"2015-06-21T16:33:51Z","abstract_excerpt":"We deal with a generalization of a Theorem of P. Gordan and M. Noether on hypersurfaces with vanishing (first) Hessian. We prove that for any given $N\\geq 3$, $d \\geq 3$ and $2\\leq k < \\frac{d}{2}$ there are infinitely many irreducible hypersurfaces $X = V(f)\\subset \\mathbb{P}^N$, of degree $\\operatorname{deg}(f)=d$, not cones and such that their Hessian determinant of order $k$, $\\operatorname{hess}^k_f$, vanishes identically. The vanishing of higher Hessians is closely related with the Strong (or Weak) Lefschetz property for standard graded Artinian Gorenstein algebra, as pointed out firstly"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06387","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"}