{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:IZ5XFPAGXVPZWSXNEIEUDQC3WV","short_pith_number":"pith:IZ5XFPAG","schema_version":"1.0","canonical_sha256":"467b72bc06bd5f9b4aed220941c05bb56cf6bc499625dd559481c0b1106892fc","source":{"kind":"arxiv","id":"1807.08918","version":1},"attestation_state":"computed","paper":{"title":"aCM vector bundles on projective surfaces of nonnegative Kodaira dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Edoardo Ballico, Joan Pons-Llopis, Sukmoon Huh","submitted_at":"2018-07-24T06:04:58Z","abstract_excerpt":"In this paper we contribute to the construction of families of arithmetically Cohen-Macaulay (aCM) indecomposable vector bundles on a wide range of polarized surfaces $(X,\\Oo_X(1))$ for $\\Oo_X(1)$ an ample line bundle. In many cases, we show that for every positive integer $r$ there exists a family of indecomposable aCM vector bundles of rank $r$, depending roughly on $r$ parameters, and in particular they are of \\emph{wild representation type}. We also introduce a general setting to study the complexity of a polarized variety $(X,\\Oo_X(1))$ with respect to its category of aCM vector bundles. "},"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":"1807.08918","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-07-24T06:04:58Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"50499592ad521ae5348ec5468210e089a825509f9722ab4638d43a2da1cc58d2","abstract_canon_sha256":"96de3e07ad37cccd644558fdfd21cc59b8a059c78b75c65a2dbe398449aed6bf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:57.428668Z","signature_b64":"C5R95puYzsjfuisuys9rJhGPwngCJkyfVj4WxBd1va0o6jLAf3tz1G6Nhms0X9vW/PSThcyWsssKUlroIw7FDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"467b72bc06bd5f9b4aed220941c05bb56cf6bc499625dd559481c0b1106892fc","last_reissued_at":"2026-05-18T00:09:57.427877Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:57.427877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"aCM vector bundles on projective surfaces of nonnegative Kodaira dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Edoardo Ballico, Joan Pons-Llopis, Sukmoon Huh","submitted_at":"2018-07-24T06:04:58Z","abstract_excerpt":"In this paper we contribute to the construction of families of arithmetically Cohen-Macaulay (aCM) indecomposable vector bundles on a wide range of polarized surfaces $(X,\\Oo_X(1))$ for $\\Oo_X(1)$ an ample line bundle. In many cases, we show that for every positive integer $r$ there exists a family of indecomposable aCM vector bundles of rank $r$, depending roughly on $r$ parameters, and in particular they are of \\emph{wild representation type}. We also introduce a general setting to study the complexity of a polarized variety $(X,\\Oo_X(1))$ with respect to its category of aCM vector bundles. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.08918","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":"1807.08918","created_at":"2026-05-18T00:09:57.428014+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.08918v1","created_at":"2026-05-18T00:09:57.428014+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.08918","created_at":"2026-05-18T00:09:57.428014+00:00"},{"alias_kind":"pith_short_12","alias_value":"IZ5XFPAGXVPZ","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_16","alias_value":"IZ5XFPAGXVPZWSXN","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_8","alias_value":"IZ5XFPAG","created_at":"2026-05-18T12:32:31.084164+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/IZ5XFPAGXVPZWSXNEIEUDQC3WV","json":"https://pith.science/pith/IZ5XFPAGXVPZWSXNEIEUDQC3WV.json","graph_json":"https://pith.science/api/pith-number/IZ5XFPAGXVPZWSXNEIEUDQC3WV/graph.json","events_json":"https://pith.science/api/pith-number/IZ5XFPAGXVPZWSXNEIEUDQC3WV/events.json","paper":"https://pith.science/paper/IZ5XFPAG"},"agent_actions":{"view_html":"https://pith.science/pith/IZ5XFPAGXVPZWSXNEIEUDQC3WV","download_json":"https://pith.science/pith/IZ5XFPAGXVPZWSXNEIEUDQC3WV.json","view_paper":"https://pith.science/paper/IZ5XFPAG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.08918&json=true","fetch_graph":"https://pith.science/api/pith-number/IZ5XFPAGXVPZWSXNEIEUDQC3WV/graph.json","fetch_events":"https://pith.science/api/pith-number/IZ5XFPAGXVPZWSXNEIEUDQC3WV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IZ5XFPAGXVPZWSXNEIEUDQC3WV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IZ5XFPAGXVPZWSXNEIEUDQC3WV/action/storage_attestation","attest_author":"https://pith.science/pith/IZ5XFPAGXVPZWSXNEIEUDQC3WV/action/author_attestation","sign_citation":"https://pith.science/pith/IZ5XFPAGXVPZWSXNEIEUDQC3WV/action/citation_signature","submit_replication":"https://pith.science/pith/IZ5XFPAGXVPZWSXNEIEUDQC3WV/action/replication_record"}},"created_at":"2026-05-18T00:09:57.428014+00:00","updated_at":"2026-05-18T00:09:57.428014+00:00"}