{"paper":{"title":"A 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":"2015-06-13T02:10:16Z","abstract_excerpt":"Let $A$ be an Artinian Gorenstein algebra over an infinite field $k$ with either $\\hbox{char}(k)=0$ or $\\hbox{char}(k)>\\nu$, where $\\nu$ is the socle degree of $A$. To every such algebra and a linear projection $\\pi$ on its maximal ideal ${\\mathfrak m}$ with range equal to the socle $\\hbox {Soc}(A)$ of $A$, one can associate a certain algebraic hypersurface $S_{\\pi}\\subset{\\mathfrak m}$, which is the graph of a polynomial map $P_{\\pi}:\\hbox{ker}\\,\\pi\\to \\hbox{Soc}(A)\\simeq k$. Recently, the author and his collaborators have obtained the following surprising criterion: two Artinian Gorenstein a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.04211","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"}