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This is done by showing that the space stratifies in smooth subvarieties, the Hilbert-Samuel's strata, each of which has an affine paving with cells of known dimension, indexed by marked Young diagrams. The affine pavings of the Hilbert-Samuel"},"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":"1609.05005","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-09-16T11:29:49Z","cross_cats_sorted":[],"title_canon_sha256":"b84e5174518728793e8d610ae81755c69174aa6a4a5dfc7c2077cdec23585d55","abstract_canon_sha256":"49f1050eb41568e91a21b0365f055fc0073448b0236aea37b33c3f208581b95f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:31.837106Z","signature_b64":"7LkjEGQPbUCRnP6ar1bfLEvuerHcKMWdvPeuaCHW1uB0of3u8NPA/VOg4+KPlZv5lJwBZ2wVDugr7KpfGq2RCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5bc7d3ac49a5681cbae0337e146e67373234c036fda2cdc7c3deb91dbaf4f284","last_reissued_at":"2026-05-18T01:04:31.836421Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:31.836421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Homology of the three flag Hilbert scheme","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Daniele Boccalini","submitted_at":"2016-09-16T11:29:49Z","abstract_excerpt":"We prove the existence of an affine paving for the three-step flag Hilbert scheme $$ \\text{Hilb}^{n, n+1, n+2}(0) := \\left\\{\\mathbb{C}[[x,y]]\\supset I_n\\supset I_{n+1}\\supset I_{n+2}: I_i \\,\\,\\text{ ideals with } \\text{dim}_{\\mathbb{C}} {\\mathbb{C}[x,y]}/{I_i} = i \\right\\} $$ of 0-dimensional subschemes that are supported at the origin of $\\mathbb{C}^2$. This is done by showing that the space stratifies in smooth subvarieties, the Hilbert-Samuel's strata, each of which has an affine paving with cells of known dimension, indexed by marked Young diagrams. 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