{"paper":{"title":"Irreducible components of module varieties: projective equations and rationality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"B. Huisgen-Zimmermann, K.R. Goodearl","submitted_at":"2011-08-14T02:10:33Z","abstract_excerpt":"We expand the existing arsenal of methods for exploring the irreducible components of the varieties $Rep(A,\\bold d)$ which parametrize the representations with dimension vector $\\bold d$ of a finite dimensional algebra $A$. To do so, we move back and forth between $Rep(A,\\bold d)$ and a projective variety, $GRASS(A,\\bold d)$, parametrizing the same set of isomorphism classes of modules. In particular, we show the irreducible components to be accessible in a highly compressed format within the projective setting. Our results include necessary and sufficient conditions for unirationality, smooth"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2833","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"}