{"paper":{"title":"Degenerations of multisingularities and Artin algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jakub Koncki, Rich\\'ard Rim\\'anyi","submitted_at":"2026-07-17T14:57:57Z","abstract_excerpt":"We study the degeneration hierarchy of commutative, associative, finite-dimensional complex Artin algebras. Instead of studying degenerations in the Hilbert scheme, we introduce a singularity-theoretic notion of degeneration based on the correspondence between singularities of stable map germs and local algebras. This leads to a natural partially ordered set, the stable hierarchy, in which one algebra degenerates to another if nearby singularities realize the latter.\n  Our first main result is that, in a wide range of dimensions, this hierarchy can be determined purely from symmetry data, name"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16022","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.16022/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}