{"paper":{"title":"Generically $\\tau$-regular irreducible components of module varieties","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Grzegorz Bobi\\'nski, Jan Schr\\\"oer","submitted_at":"2025-02-19T13:25:00Z","abstract_excerpt":"In the representation theory of finite-dimensional algebras, the study of projective presentations of maximal rank is closely related to the study of generically $\\tau$-regular irreducible components of varieties of modules over such algebras. We show that a module is $\\tau$-regular if and only if its minimal projective presentation is of maximal rank. This is a refinement of a theorem by Plamondon. We prove that generic extensions of generically $\\tau$-regular components by simple projective modules are again generically $\\tau$-regular. This leads to the classification of all generically $\\ta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.13709","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"}