{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:MGNDHVCX3ZW7MH2MHBR4OOZLXZ","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":"36f1150ae3a2ae7ad57422bedfc80b4dbe2ab2010ce9c796ed66c6c8144dda5a","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2003-10-02T16:17:53Z","title_canon_sha256":"2454b5f2ddcc12d820cd7b5dae60d2fefeafe9e8651d1f2430852bad17be8ead"},"schema_version":"1.0","source":{"id":"math/0310026","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0310026","created_at":"2026-05-18T03:51:47Z"},{"alias_kind":"arxiv_version","alias_value":"math/0310026v2","created_at":"2026-05-18T03:51:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0310026","created_at":"2026-05-18T03:51:47Z"},{"alias_kind":"pith_short_12","alias_value":"MGNDHVCX3ZW7","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"MGNDHVCX3ZW7MH2M","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"MGNDHVCX","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:623157ce0fe17cfe67f889bce168e99d53c78dc7dafceb203d467da68a6c1474","target":"graph","created_at":"2026-05-18T03:51:47Z","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"},"paper":{"abstract_excerpt":"In the first part of this paper we prove a vanishing criterion for higher direct images of projective families of line bundles on a Cohen-Macaulay variety X. The result involves certain first-order deformations of certain curves on X, and makes essential use of the notion of global co-gaussian maps, a generalization of Wahl's gaussian maps. In the second part we apply the criterion above, combined with Fourier-Mukai transform on abelian varieties, to prove an algebraic version of Green-Lazarsfeld's Generic Vanishing Theorem. In fact we prove a stronger result concerning higher direct images of","authors_text":"Giuseppe Pareschi","cross_cats":[],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2003-10-02T16:17:53Z","title":"Generic vanishing, gaussian maps, and Fourier-Mukai transform"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0310026","kind":"arxiv","version":2},"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:b7dc1a03a62b361529660552eb8e98aeb43d92c60747c30e232df4acd62d3079","target":"record","created_at":"2026-05-18T03:51:47Z","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":"36f1150ae3a2ae7ad57422bedfc80b4dbe2ab2010ce9c796ed66c6c8144dda5a","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2003-10-02T16:17:53Z","title_canon_sha256":"2454b5f2ddcc12d820cd7b5dae60d2fefeafe9e8651d1f2430852bad17be8ead"},"schema_version":"1.0","source":{"id":"math/0310026","kind":"arxiv","version":2}},"canonical_sha256":"619a33d457de6df61f4c3863c73b2bbe66c4c9d2315513f970b031101c5d5ea2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"619a33d457de6df61f4c3863c73b2bbe66c4c9d2315513f970b031101c5d5ea2","first_computed_at":"2026-05-18T03:51:47.539485Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:47.539485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yZ4EociNy4etXdxNU9YIWBB49rVhnDoaYXIwDTCk6brdU3FWWBfs5qILKWt78xEROOyNZQv4/0dubBXVKGSXAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:47.540263Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0310026","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7dc1a03a62b361529660552eb8e98aeb43d92c60747c30e232df4acd62d3079","sha256:623157ce0fe17cfe67f889bce168e99d53c78dc7dafceb203d467da68a6c1474"],"state_sha256":"b3da21031a3c5be31eb418c9e80e365a9c4b7115e78badde7510a563635d3ec7"}