{"paper":{"title":"On the singularity of the irreducible components of a Springer fiber in sl(n)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Anna Melnikov, Lucas Fresse","submitted_at":"2009-05-11T13:34:20Z","abstract_excerpt":"Let ${\\mathcal B}_u$ be the Springer fiber over a nilpotent endomorphism $u\\in End(\\mathbb{C}^n)$. Let $J(u)$ be the Jordan form of $u$ regarded as a partition of $n$. The irreducible components of ${\\mathcal B}_u$ are all of the same dimension. They are labelled by Young tableaux of shape $J(u)$. We study the question of singularity of the components of ${\\mathcal B}_u$ and show that all the components of ${\\mathcal B}_u$ are nonsingular if and only if $J(u)\\in\\{(\\lambda,1,1,...), (\\lambda_1,\\lambda_2), (\\lambda_1,\\lambda_2,1), (2,2,2)\\}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.1617","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"}