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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 $J(u)\\in\\{(\\lambda,1,1,...), (\\lambda_1,\\lambda_2), (\\lambda_1,\\lambda_2,1), (2,2,2)\\}$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0905.1617","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-05-11T13:34:20Z","cross_cats_sorted":[],"title_canon_sha256":"492bf2ab0ff018f8320c016897f68a05893a9f9c01309004bdf369a6400a0b91","abstract_canon_sha256":"b1cbff6c6d7f6ce4b03003f1e0250123db4c6544a0f9211f2230f0f5331027c7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:20.630867Z","signature_b64":"GDAyZc558gcDC3qNjFvnY4WTIH5au2YX9sCQTK3aAa/6L6xsGbSZR5npsNFs8XixI7gZVrIaOeHK0HwwCACMCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"821ce9c60b98f1897bf21b269f94a3510855b28fd8f241704cf8db06d4d257eb","last_reissued_at":"2026-05-18T04:40:20.630310Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:20.630310Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $u\\in End(\\mathbb{C}^n)$. 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