{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:B3IXQCKVSPVY6IEKTNTDF22V76","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"ef02a417c6ecf733d53c25c75ab3c68bd0b1d31b82b2ca561aa4031530b8dbe6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-03-05T17:24:16Z","title_canon_sha256":"efec7a98dc3b1800420763df9bd7bd4033018f50fdd42adf40fdcf5ad0d649f0"},"schema_version":"1.0","source":{"id":"2403.03139","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.03139","created_at":"2026-07-05T07:52:36Z"},{"alias_kind":"arxiv_version","alias_value":"2403.03139v1","created_at":"2026-07-05T07:52:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.03139","created_at":"2026-07-05T07:52:36Z"},{"alias_kind":"pith_short_12","alias_value":"B3IXQCKVSPVY","created_at":"2026-07-05T07:52:36Z"},{"alias_kind":"pith_short_16","alias_value":"B3IXQCKVSPVY6IEK","created_at":"2026-07-05T07:52:36Z"},{"alias_kind":"pith_short_8","alias_value":"B3IXQCKV","created_at":"2026-07-05T07:52:36Z"}],"graph_snapshots":[{"event_id":"sha256:4b7575e48b502398feafc8772b5745c09755230a0d8b045103c1d4d0ea0f6344","target":"graph","created_at":"2026-07-05T07:52:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2403.03139/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the positivity of an Ulrich vector bundle defined with respect to a globally generated ample line bundle. First we prove a generalization of a Lopez theorem on the first Chern class and the bigness of an Ulrich bundle. Then, under some additional assumptions on the polarization, we give a description of its augmented base locus, which consequently leads to a characterization of the V-bigness and of the ampleness of an Ulrich bundle in this setting.","authors_text":"Valerio Buttinelli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-03-05T17:24:16Z","title":"Positivity of Ulrich bundles in the ample and free case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.03139","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:4c0e890f90198326892b314a1902a257071cc69bbf300574aca173f6c916c62e","target":"record","created_at":"2026-07-05T07:52:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ef02a417c6ecf733d53c25c75ab3c68bd0b1d31b82b2ca561aa4031530b8dbe6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-03-05T17:24:16Z","title_canon_sha256":"efec7a98dc3b1800420763df9bd7bd4033018f50fdd42adf40fdcf5ad0d649f0"},"schema_version":"1.0","source":{"id":"2403.03139","kind":"arxiv","version":1}},"canonical_sha256":"0ed178095593eb8f208a9b6632eb55ffa096033efa7ecef1a305ab42dfed30f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ed178095593eb8f208a9b6632eb55ffa096033efa7ecef1a305ab42dfed30f2","first_computed_at":"2026-07-05T07:52:36.501075Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:52:36.501075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n43JrjNKIAj0OPqVZEEHjyR5Wk5rXf7E5rlOxrrFrqHEM+QG2L9Siy0ZhskiDLhML2+IENRGf0z+QKoQrFtkCw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:52:36.501503Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.03139","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c0e890f90198326892b314a1902a257071cc69bbf300574aca173f6c916c62e","sha256:4b7575e48b502398feafc8772b5745c09755230a0d8b045103c1d4d0ea0f6344"],"state_sha256":"e945df5ec31702671e589594638babaedc151d34b54c29b768960bd40432b5de"}