{"paper":{"title":"On the Affine Homogeneity of Algebraic Hypersurfaces Arising from Gorenstein Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CV","math.DG"],"primary_cat":"math.AC","authors_text":"Alexander Isaev","submitted_at":"2011-01-03T04:12:41Z","abstract_excerpt":"To every Gorenstein algebra $A$ of finite dimension greater than 1 over a field ${\\Bbb F}$ of characteristic zero, and a projection $\\pi$ on its maximal ideal ${\\mathfrak m}$ with range equal to the annihilator $\\hbox{Ann}({\\mathfrak m})$ of ${\\mathfrak m}$, one can associate a certain algebraic hypersurface $S_{\\pi}\\subset{\\mathfrak m}$. Such hypersurfaces possess remarkable properties. They can be used, for instance, to help decide whether two given Gorenstein algebras are isomorphic, which for ${\\Bbb F}={\\Bbb C}$ leads to interesting consequences in singularity theory. Also, for ${\\Bbb F}={"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.0452","kind":"arxiv","version":3},"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"}