{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:2O4GPQMZBFBB7Z2ZDUOWBMUXYG","short_pith_number":"pith:2O4GPQMZ","schema_version":"1.0","canonical_sha256":"d3b867c19909421fe7591d1d60b297c1b06634584f04a108154a1b754780437a","source":{"kind":"arxiv","id":"1710.04652","version":1},"attestation_state":"computed","paper":{"title":"Fourier-Mukai transforms of slope stable torsion-free sheaves on Weierstrass elliptic surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jason Lo","submitted_at":"2017-10-12T09:07:37Z","abstract_excerpt":"On a Weierstra{\\ss} elliptic surface $X$, we define a `limit' of Bridgeland stability conditions, denoted $Z^l$-stability, by varying the polarisation in the definition of Bridgeland stability along a curve in the ample cone of $X$. We show that a slope stable torsion-free sheaf of positive (twisted) degree or a slope stable locally free sheaf is taken by a Fourier-Mukai transform on $D^b(X)$ to a $Z^l$-stable object, while a $Z^l$-semistable object of nonzero fiber degree can be modified so that its inverse Fourier-Mukai transform is a slope semistable torsion-free sheaf."},"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":"1710.04652","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-10-12T09:07:37Z","cross_cats_sorted":[],"title_canon_sha256":"cb86f2632673da4d6304efec806b0ad4ffdca1d1d371c5548f83ae2d3710c9d4","abstract_canon_sha256":"cecb39a6315a28ab01e610335b77ad34894e4405438f8405d6b1bd2b6b785a9a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:57.084012Z","signature_b64":"tLfZBmRo5CUVyIsd7peM1+03ci2bdM+IKBh4rhiGgy17yD8vCtR8x05ZkIMudqMyEj28O9KdB3yKQSA5K/c6CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d3b867c19909421fe7591d1d60b297c1b06634584f04a108154a1b754780437a","last_reissued_at":"2026-05-18T00:32:57.083401Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:57.083401Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fourier-Mukai transforms of slope stable torsion-free sheaves on Weierstrass elliptic surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jason Lo","submitted_at":"2017-10-12T09:07:37Z","abstract_excerpt":"On a Weierstra{\\ss} elliptic surface $X$, we define a `limit' of Bridgeland stability conditions, denoted $Z^l$-stability, by varying the polarisation in the definition of Bridgeland stability along a curve in the ample cone of $X$. We show that a slope stable torsion-free sheaf of positive (twisted) degree or a slope stable locally free sheaf is taken by a Fourier-Mukai transform on $D^b(X)$ to a $Z^l$-stable object, while a $Z^l$-semistable object of nonzero fiber degree can be modified so that its inverse Fourier-Mukai transform is a slope semistable torsion-free sheaf."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.04652","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":"1710.04652","created_at":"2026-05-18T00:32:57.083489+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.04652v1","created_at":"2026-05-18T00:32:57.083489+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.04652","created_at":"2026-05-18T00:32:57.083489+00:00"},{"alias_kind":"pith_short_12","alias_value":"2O4GPQMZBFBB","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_16","alias_value":"2O4GPQMZBFBB7Z2Z","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_8","alias_value":"2O4GPQMZ","created_at":"2026-05-18T12:30:55.937587+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/2O4GPQMZBFBB7Z2ZDUOWBMUXYG","json":"https://pith.science/pith/2O4GPQMZBFBB7Z2ZDUOWBMUXYG.json","graph_json":"https://pith.science/api/pith-number/2O4GPQMZBFBB7Z2ZDUOWBMUXYG/graph.json","events_json":"https://pith.science/api/pith-number/2O4GPQMZBFBB7Z2ZDUOWBMUXYG/events.json","paper":"https://pith.science/paper/2O4GPQMZ"},"agent_actions":{"view_html":"https://pith.science/pith/2O4GPQMZBFBB7Z2ZDUOWBMUXYG","download_json":"https://pith.science/pith/2O4GPQMZBFBB7Z2ZDUOWBMUXYG.json","view_paper":"https://pith.science/paper/2O4GPQMZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.04652&json=true","fetch_graph":"https://pith.science/api/pith-number/2O4GPQMZBFBB7Z2ZDUOWBMUXYG/graph.json","fetch_events":"https://pith.science/api/pith-number/2O4GPQMZBFBB7Z2ZDUOWBMUXYG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2O4GPQMZBFBB7Z2ZDUOWBMUXYG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2O4GPQMZBFBB7Z2ZDUOWBMUXYG/action/storage_attestation","attest_author":"https://pith.science/pith/2O4GPQMZBFBB7Z2ZDUOWBMUXYG/action/author_attestation","sign_citation":"https://pith.science/pith/2O4GPQMZBFBB7Z2ZDUOWBMUXYG/action/citation_signature","submit_replication":"https://pith.science/pith/2O4GPQMZBFBB7Z2ZDUOWBMUXYG/action/replication_record"}},"created_at":"2026-05-18T00:32:57.083489+00:00","updated_at":"2026-05-18T00:32:57.083489+00:00"}