{"paper":{"title":"Varieties of uniserial representations IV. Kinship to geometric quotients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Birge Huisgen-Zimmermann, Klaus Bongartz","submitted_at":"2014-07-08T23:26:07Z","abstract_excerpt":"Let $\\Lambda$ be a finite dimensional algebra over an algebraically closed field, and ${\\Bbb S}$ a finite sequence of simple left $\\Lambda$-modules. In [6, 9], quasiprojective algebraic varieties with accessible affine open covers were introduced, for use in classifying the uniserial representations of $\\Lambda$ having sequence ${\\Bbb S}$ of consecutive composition factors. Our principal objectives here are threefold: One is to prove these varieties to be `good approximations' -- in a sense to be made precise -- to geometric quotients of the classical varieties $\\operatorname{Mod-Uni}({\\Bbb S}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2296","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"}