{"paper":{"title":"On a new criterion for isomorphism of Artinian Gorenstein algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"A. V. Isaev","submitted_at":"2012-01-30T03:00:45Z","abstract_excerpt":"To every Gorenstein algebra $A$ of finite vector space dimension greater than 1 over a field $\\FF$ of characteristic zero, and a linear projection $\\pi$ on its maximal ideal ${\\mathfrak m}$ with range equal to the annihilator $\\Ann({\\mathfrak m})$ of ${\\mathfrak m}$, one can associate a certain algebraic hypersurface $S_{\\pi}\\subset{\\mathfrak m}$, which is the graph of a polynomial map $P_{\\pi}:\\ker\\pi\\ra\\Ann({\\mathfrak m})\\simeq\\FF$. Recently, in {\\rm\\cite{FIKK}}, {\\rm\\cite{FK}} the following surprising criterion was obtained: two Gorenstein algebras $A$, $\\tilde A$ are isomorphic if and only"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.6100","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"}