{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:VMBEAVV6PWGXZSRNPBHORJLEMP","short_pith_number":"pith:VMBEAVV6","schema_version":"1.0","canonical_sha256":"ab024056be7d8d7cca2d784ee8a56463d04acff3ca3625bc8238baed2906b8de","source":{"kind":"arxiv","id":"1110.4711","version":1},"attestation_state":"computed","paper":{"title":"Principal part bundles on $\\PP^n$ and quiver representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Riccardo Re","submitted_at":"2011-10-21T07:10:53Z","abstract_excerpt":"We study the principal parts bundles $P^k (L)$ of the degree $d$ line bundle $L$ on the $n$ dimensional projective space as homogeneous bundles and we describe their associated quiver representations. We use this approach to show that if $n$ is greater or equal that 2, and $0\\leq d<k$, then there exists an invariant splitting $P^k(L)=Q\\oplus (S^dV\\otimes \\OO_{\\PP^n})$ with $Q$ a stable homogeneous vector bundle. The splitting properties of such bundles were previously known only for n=1 or $k\\leq d$ or $d<0$. Moreover we show that for any $d$ and any $h<k$ the canonical map from $P^k(L)$ to $P"},"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":"1110.4711","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-10-21T07:10:53Z","cross_cats_sorted":[],"title_canon_sha256":"c10b8b6b93f217559344c7e1e13c9805bd64b46b28f1d6d854a359461a40776d","abstract_canon_sha256":"70b6de565c63318eb9d4c966c8e3e5c7888f2fa2a02defd9550a64dde16b4e93"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:35.242704Z","signature_b64":"SQu4A2u4NOjR5RULPZVJZz0dska3j8XUbI9Kgs0/3ZIrzMut+/lIcveeaF+wrw5eSWVHtriHTMNUPexaf+YCAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab024056be7d8d7cca2d784ee8a56463d04acff3ca3625bc8238baed2906b8de","last_reissued_at":"2026-05-18T04:10:35.242109Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:35.242109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Principal part bundles on $\\PP^n$ and quiver representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Riccardo Re","submitted_at":"2011-10-21T07:10:53Z","abstract_excerpt":"We study the principal parts bundles $P^k (L)$ of the degree $d$ line bundle $L$ on the $n$ dimensional projective space as homogeneous bundles and we describe their associated quiver representations. We use this approach to show that if $n$ is greater or equal that 2, and $0\\leq d<k$, then there exists an invariant splitting $P^k(L)=Q\\oplus (S^dV\\otimes \\OO_{\\PP^n})$ with $Q$ a stable homogeneous vector bundle. The splitting properties of such bundles were previously known only for n=1 or $k\\leq d$ or $d<0$. Moreover we show that for any $d$ and any $h<k$ the canonical map from $P^k(L)$ to $P"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4711","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":""},"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":"1110.4711","created_at":"2026-05-18T04:10:35.242186+00:00"},{"alias_kind":"arxiv_version","alias_value":"1110.4711v1","created_at":"2026-05-18T04:10:35.242186+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.4711","created_at":"2026-05-18T04:10:35.242186+00:00"},{"alias_kind":"pith_short_12","alias_value":"VMBEAVV6PWGX","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_16","alias_value":"VMBEAVV6PWGXZSRN","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_8","alias_value":"VMBEAVV6","created_at":"2026-05-18T12:26:44.992195+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/VMBEAVV6PWGXZSRNPBHORJLEMP","json":"https://pith.science/pith/VMBEAVV6PWGXZSRNPBHORJLEMP.json","graph_json":"https://pith.science/api/pith-number/VMBEAVV6PWGXZSRNPBHORJLEMP/graph.json","events_json":"https://pith.science/api/pith-number/VMBEAVV6PWGXZSRNPBHORJLEMP/events.json","paper":"https://pith.science/paper/VMBEAVV6"},"agent_actions":{"view_html":"https://pith.science/pith/VMBEAVV6PWGXZSRNPBHORJLEMP","download_json":"https://pith.science/pith/VMBEAVV6PWGXZSRNPBHORJLEMP.json","view_paper":"https://pith.science/paper/VMBEAVV6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1110.4711&json=true","fetch_graph":"https://pith.science/api/pith-number/VMBEAVV6PWGXZSRNPBHORJLEMP/graph.json","fetch_events":"https://pith.science/api/pith-number/VMBEAVV6PWGXZSRNPBHORJLEMP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VMBEAVV6PWGXZSRNPBHORJLEMP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VMBEAVV6PWGXZSRNPBHORJLEMP/action/storage_attestation","attest_author":"https://pith.science/pith/VMBEAVV6PWGXZSRNPBHORJLEMP/action/author_attestation","sign_citation":"https://pith.science/pith/VMBEAVV6PWGXZSRNPBHORJLEMP/action/citation_signature","submit_replication":"https://pith.science/pith/VMBEAVV6PWGXZSRNPBHORJLEMP/action/replication_record"}},"created_at":"2026-05-18T04:10:35.242186+00:00","updated_at":"2026-05-18T04:10:35.242186+00:00"}