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We show that $S^{[n,m]}$, $S^{[n,m,m+1]}$, $S^{[n,n+1,m]}$, $S^{[n,n+1,m,m+1]}$, $S^{[n,n+2,m]}$ and $S^{[n,n+2,m,m+1]}$ are irreducible."},"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":"2209.09003","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2022-09-19T13:27:02Z","cross_cats_sorted":[],"title_canon_sha256":"63a4c80d226432718f79709f42103ca6900c4645faf063258c115606c1b09805","abstract_canon_sha256":"9dfb41c60922c87940d193be1f09e3f6fce4c0c040342ee575e13d686b6e47ed"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:07:04.950179Z","signature_b64":"pieaICrbV91mc02m2fZ563sBAs2gTDa51Y7U7QteO2Ez+hmtyYA5nHIqfZuxz3IBYsgHEQRIuXyWADX6itpHCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"532c9153af67aaaeb2ee0286cf29ec83873192e43cfb724390f0512dd9bc5f1c","last_reissued_at":"2026-07-05T07:07:04.949631Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:07:04.949631Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Irreducibility of Some Nested Hilbert Schemes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Chandranandan Gangopadhyay, Parvez Rasul, Ronnie Sebastian","submitted_at":"2022-09-19T13:27:02Z","abstract_excerpt":"Let $S$ be a smooth projective surface over $\\mathbb{C}$. Let $S^{[n_1,\\dots,n_k]}$ denote the nested Hilbert scheme which parametrizes zero-dimensional subschemes $\\xi_{n_1} \\subset \\ldots \\subset \\xi_{n_k}$ where $\\xi_i$ is a closed subscheme of $S$ of length $i$. We show that $S^{[n,m]}$, $S^{[n,m,m+1]}$, $S^{[n,n+1,m]}$, $S^{[n,n+1,m,m+1]}$, $S^{[n,n+2,m]}$ and $S^{[n,n+2,m,m+1]}$ are irreducible."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.09003","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2209.09003/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2209.09003","created_at":"2026-07-05T07:07:04.949688+00:00"},{"alias_kind":"arxiv_version","alias_value":"2209.09003v2","created_at":"2026-07-05T07:07:04.949688+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.09003","created_at":"2026-07-05T07:07:04.949688+00:00"},{"alias_kind":"pith_short_12","alias_value":"KMWJCU5PM6VK","created_at":"2026-07-05T07:07:04.949688+00:00"},{"alias_kind":"pith_short_16","alias_value":"KMWJCU5PM6VK5MXO","created_at":"2026-07-05T07:07:04.949688+00:00"},{"alias_kind":"pith_short_8","alias_value":"KMWJCU5P","created_at":"2026-07-05T07:07:04.949688+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KMWJCU5PM6VK5MXOAKDM6KPMQO","json":"https://pith.science/pith/KMWJCU5PM6VK5MXOAKDM6KPMQO.json","graph_json":"https://pith.science/api/pith-number/KMWJCU5PM6VK5MXOAKDM6KPMQO/graph.json","events_json":"https://pith.science/api/pith-number/KMWJCU5PM6VK5MXOAKDM6KPMQO/events.json","paper":"https://pith.science/paper/KMWJCU5P"},"agent_actions":{"view_html":"https://pith.science/pith/KMWJCU5PM6VK5MXOAKDM6KPMQO","download_json":"https://pith.science/pith/KMWJCU5PM6VK5MXOAKDM6KPMQO.json","view_paper":"https://pith.science/paper/KMWJCU5P","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2209.09003&json=true","fetch_graph":"https://pith.science/api/pith-number/KMWJCU5PM6VK5MXOAKDM6KPMQO/graph.json","fetch_events":"https://pith.science/api/pith-number/KMWJCU5PM6VK5MXOAKDM6KPMQO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KMWJCU5PM6VK5MXOAKDM6KPMQO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KMWJCU5PM6VK5MXOAKDM6KPMQO/action/storage_attestation","attest_author":"https://pith.science/pith/KMWJCU5PM6VK5MXOAKDM6KPMQO/action/author_attestation","sign_citation":"https://pith.science/pith/KMWJCU5PM6VK5MXOAKDM6KPMQO/action/citation_signature","submit_replication":"https://pith.science/pith/KMWJCU5PM6VK5MXOAKDM6KPMQO/action/replication_record"}},"created_at":"2026-07-05T07:07:04.949688+00:00","updated_at":"2026-07-05T07:07:04.949688+00:00"}