{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1995:4EB456KNF5RNXDFFLUYBV6FODK","short_pith_number":"pith:4EB456KN","schema_version":"1.0","canonical_sha256":"e103cef94d2f62db8ca55d301af8ae1a84920558161e500661bad331745cd2ab","source":{"kind":"arxiv","id":"alg-geom/9502008","version":1},"attestation_state":"computed","paper":{"title":"On singularities of  ${\\cal M}_{I\\!\\! P^3}(c_1,c_2)$","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"alg-geom","authors_text":"Giorgio Ottaviani, Vincenzo Ancona","submitted_at":"1995-02-13T17:18:43Z","abstract_excerpt":"Let ${\\cal M}_{I\\!\\! P^3}(c_1,c_2)$ be  the moduli space of stable rank-$2$ vector bundles on $I\\!\\! P^3$ with Chern classes $c_1$, $ c_2$. We prove the following results.\n  1) Let  $0 \\le \\beta < \\gamma $  be two integers, ($\\gamma \\ge 2)$, such that $2\\gamma-3\\beta>0$; then ${\\cal M}_{I\\!\\! P^3}(0,2\\gamma^2-3\\beta^2)$ is singular (the case $\\beta =0$ was previously proved by M. Maggesi).\n  2) Let $0 \\le \\beta < \\gamma $  be two odd integers ($\\gamma \\ge 5)$, such that $2\\gamma-3\\beta+1>0$; then ${\\cal M}_{I\\!\\! P^3}(-1,2(\\gamma/2)^2-3(\\beta/2)^2+1/4)$  is singular.\n  In particular ${\\cal M}_"},"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":"alg-geom/9502008","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"alg-geom","submitted_at":"1995-02-13T17:18:43Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"e4e98ffa9ed0ad22fbd0ecd0987dc9f0148ef33a6020f0080b820b7bc9dd435e","abstract_canon_sha256":"7ca385f5ca740436629e8e77c6422a3db6f02005067725da4927c2cc440b7f8d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:42.993884Z","signature_b64":"xC1I3qscoucqZ4UKgW28Uva9OJVxpv8SLuqcIhXoKzIk5DKTmx29McI5JNC3upeoLXjYMu1+MD9xydqUR50BDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e103cef94d2f62db8ca55d301af8ae1a84920558161e500661bad331745cd2ab","last_reissued_at":"2026-05-18T01:37:42.993451Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:42.993451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On singularities of  ${\\cal M}_{I\\!\\! P^3}(c_1,c_2)$","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"alg-geom","authors_text":"Giorgio Ottaviani, Vincenzo Ancona","submitted_at":"1995-02-13T17:18:43Z","abstract_excerpt":"Let ${\\cal M}_{I\\!\\! P^3}(c_1,c_2)$ be  the moduli space of stable rank-$2$ vector bundles on $I\\!\\! P^3$ with Chern classes $c_1$, $ c_2$. We prove the following results.\n  1) Let  $0 \\le \\beta < \\gamma $  be two integers, ($\\gamma \\ge 2)$, such that $2\\gamma-3\\beta>0$; then ${\\cal M}_{I\\!\\! P^3}(0,2\\gamma^2-3\\beta^2)$ is singular (the case $\\beta =0$ was previously proved by M. Maggesi).\n  2) Let $0 \\le \\beta < \\gamma $  be two odd integers ($\\gamma \\ge 5)$, such that $2\\gamma-3\\beta+1>0$; then ${\\cal M}_{I\\!\\! P^3}(-1,2(\\gamma/2)^2-3(\\beta/2)^2+1/4)$  is singular.\n  In particular ${\\cal M}_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9502008","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":"alg-geom/9502008","created_at":"2026-05-18T01:37:42.993522+00:00"},{"alias_kind":"arxiv_version","alias_value":"alg-geom/9502008v1","created_at":"2026-05-18T01:37:42.993522+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.alg-geom/9502008","created_at":"2026-05-18T01:37:42.993522+00:00"},{"alias_kind":"pith_short_12","alias_value":"4EB456KNF5RN","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_16","alias_value":"4EB456KNF5RNXDFF","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_8","alias_value":"4EB456KN","created_at":"2026-05-18T12:25:47.102015+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/4EB456KNF5RNXDFFLUYBV6FODK","json":"https://pith.science/pith/4EB456KNF5RNXDFFLUYBV6FODK.json","graph_json":"https://pith.science/api/pith-number/4EB456KNF5RNXDFFLUYBV6FODK/graph.json","events_json":"https://pith.science/api/pith-number/4EB456KNF5RNXDFFLUYBV6FODK/events.json","paper":"https://pith.science/paper/4EB456KN"},"agent_actions":{"view_html":"https://pith.science/pith/4EB456KNF5RNXDFFLUYBV6FODK","download_json":"https://pith.science/pith/4EB456KNF5RNXDFFLUYBV6FODK.json","view_paper":"https://pith.science/paper/4EB456KN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=alg-geom/9502008&json=true","fetch_graph":"https://pith.science/api/pith-number/4EB456KNF5RNXDFFLUYBV6FODK/graph.json","fetch_events":"https://pith.science/api/pith-number/4EB456KNF5RNXDFFLUYBV6FODK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4EB456KNF5RNXDFFLUYBV6FODK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4EB456KNF5RNXDFFLUYBV6FODK/action/storage_attestation","attest_author":"https://pith.science/pith/4EB456KNF5RNXDFFLUYBV6FODK/action/author_attestation","sign_citation":"https://pith.science/pith/4EB456KNF5RNXDFFLUYBV6FODK/action/citation_signature","submit_replication":"https://pith.science/pith/4EB456KNF5RNXDFFLUYBV6FODK/action/replication_record"}},"created_at":"2026-05-18T01:37:42.993522+00:00","updated_at":"2026-05-18T01:37:42.993522+00:00"}