{"paper":{"title":"The geometry of uniserial representations of finite dimensional algebras I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Birge Huisgen-Zimmermann","submitted_at":"2014-07-09T08:27:32Z","abstract_excerpt":"It is shown that, given any finite dimensional, split basic algebra $\\Lambda = K\\Gamma/I$ (where $\\Gamma$ is a quiver and $I$ an admissible ideal in the path algebra $K \\Gamma$), there is a finite list of affine algebraic varieties, the points of which correspond in a natural fashion to the isomorphism types of uniserial left $\\Lambda$-modules, and the geometry of which faithfully reflects the constraints met in constructing such modules. A constructive coordinatized access to these varieties is given, as well as to the accompanying natural surjections from the varieties onto families of unise"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2384","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"}