{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:XUU5KFLBVI2XQP2ALIJLX2ZYC7","short_pith_number":"pith:XUU5KFLB","schema_version":"1.0","canonical_sha256":"bd29d51561aa35783f405a12bbeb3817ced05a6e20d5de4745d180b7cc9f128a","source":{"kind":"arxiv","id":"1711.03413","version":3},"attestation_state":"computed","paper":{"title":"Stability of tangent bundles of complete intersections and effective restriction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jie Liu","submitted_at":"2017-11-09T15:09:22Z","abstract_excerpt":"For $n\\geq 3$, let $M$ be an $(n+r)$-dimensional irreducible Hermitian symmetric space of compact type and let $\\mathcal{O}_M(1)$ be the ample generator of $Pic(M)$. Let $Y=H_1\\cap\\dots\\cap H_r$ be a smooth complete intersection of dimension $n$ where $H_i\\in\\vert \\mathcal{O}_M(d_i)\\vert$ with $d_i\\geq 2$. We prove a vanishing theorem for twisted holomorphic forms on $Y$. As an application, we show that the tangent bundle $T_Y$ of $Y$ is stable. Moreover, if $X$ is a smooth hypersurface of degree $d$ in $Y$ such that the restriction $Pic(Y)\\rightarrow Pic(X)$ is surjective, we establish some e"},"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":"1711.03413","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-11-09T15:09:22Z","cross_cats_sorted":[],"title_canon_sha256":"c84347f7e27976e461ce3b55ed52cfeb905b114bdb181d00bea788a3190c02a9","abstract_canon_sha256":"f63e78ffde6487680a09724b1bc87dd1379c79c587e08d711861509fea545a7a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:45.463225Z","signature_b64":"TXyO8E3lbtVfaMa0b2cwmk/WfOqhAsFC0cEYKOzhSuNTz0qCQmf9CxrbM5iHKsULFpEf1ukmYugJoX//ycDrDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd29d51561aa35783f405a12bbeb3817ced05a6e20d5de4745d180b7cc9f128a","last_reissued_at":"2026-05-18T00:02:45.462853Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:45.462853Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stability of tangent bundles of complete intersections and effective restriction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jie Liu","submitted_at":"2017-11-09T15:09:22Z","abstract_excerpt":"For $n\\geq 3$, let $M$ be an $(n+r)$-dimensional irreducible Hermitian symmetric space of compact type and let $\\mathcal{O}_M(1)$ be the ample generator of $Pic(M)$. Let $Y=H_1\\cap\\dots\\cap H_r$ be a smooth complete intersection of dimension $n$ where $H_i\\in\\vert \\mathcal{O}_M(d_i)\\vert$ with $d_i\\geq 2$. We prove a vanishing theorem for twisted holomorphic forms on $Y$. As an application, we show that the tangent bundle $T_Y$ of $Y$ is stable. Moreover, if $X$ is a smooth hypersurface of degree $d$ in $Y$ such that the restriction $Pic(Y)\\rightarrow Pic(X)$ is surjective, we establish some e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.03413","kind":"arxiv","version":3},"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":"1711.03413","created_at":"2026-05-18T00:02:45.462902+00:00"},{"alias_kind":"arxiv_version","alias_value":"1711.03413v3","created_at":"2026-05-18T00:02:45.462902+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.03413","created_at":"2026-05-18T00:02:45.462902+00:00"},{"alias_kind":"pith_short_12","alias_value":"XUU5KFLBVI2X","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_16","alias_value":"XUU5KFLBVI2XQP2A","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_8","alias_value":"XUU5KFLB","created_at":"2026-05-18T12:31:56.362134+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/XUU5KFLBVI2XQP2ALIJLX2ZYC7","json":"https://pith.science/pith/XUU5KFLBVI2XQP2ALIJLX2ZYC7.json","graph_json":"https://pith.science/api/pith-number/XUU5KFLBVI2XQP2ALIJLX2ZYC7/graph.json","events_json":"https://pith.science/api/pith-number/XUU5KFLBVI2XQP2ALIJLX2ZYC7/events.json","paper":"https://pith.science/paper/XUU5KFLB"},"agent_actions":{"view_html":"https://pith.science/pith/XUU5KFLBVI2XQP2ALIJLX2ZYC7","download_json":"https://pith.science/pith/XUU5KFLBVI2XQP2ALIJLX2ZYC7.json","view_paper":"https://pith.science/paper/XUU5KFLB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1711.03413&json=true","fetch_graph":"https://pith.science/api/pith-number/XUU5KFLBVI2XQP2ALIJLX2ZYC7/graph.json","fetch_events":"https://pith.science/api/pith-number/XUU5KFLBVI2XQP2ALIJLX2ZYC7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XUU5KFLBVI2XQP2ALIJLX2ZYC7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XUU5KFLBVI2XQP2ALIJLX2ZYC7/action/storage_attestation","attest_author":"https://pith.science/pith/XUU5KFLBVI2XQP2ALIJLX2ZYC7/action/author_attestation","sign_citation":"https://pith.science/pith/XUU5KFLBVI2XQP2ALIJLX2ZYC7/action/citation_signature","submit_replication":"https://pith.science/pith/XUU5KFLBVI2XQP2ALIJLX2ZYC7/action/replication_record"}},"created_at":"2026-05-18T00:02:45.462902+00:00","updated_at":"2026-05-18T00:02:45.462902+00:00"}