{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4NJ3IGDHT6HTLV7CL6CPURWODD","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":"99750e540c6a129b910d181e977aa25b53e2660a60c8163bea3d936f193df100","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-06-12T08:27:45Z","title_canon_sha256":"0641c418f2b92922a35931e8eccea2e3233e2e05dd32b5d3bb12501b8de01335"},"schema_version":"1.0","source":{"id":"1706.03508","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.03508","created_at":"2026-05-18T00:16:45Z"},{"alias_kind":"arxiv_version","alias_value":"1706.03508v3","created_at":"2026-05-18T00:16:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.03508","created_at":"2026-05-18T00:16:45Z"},{"alias_kind":"pith_short_12","alias_value":"4NJ3IGDHT6HT","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4NJ3IGDHT6HTLV7C","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4NJ3IGDH","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:ec37d798b62e1ce45e932558ccaa84deacc70780b2dc3d924540ec5adc164e4b","target":"graph","created_at":"2026-05-18T00:16:45Z","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":"We show that vanishing of asymptotic p-th syzygies implies p-very ampleness for line bundles on arbitrary projective schemes. For smooth surfaces we prove that the converse holds when p is small, by studying the Bridgeland-King-Reid-Haiman correspondence for tautological bundles on the Hilbert scheme of points. This extends previous results of Ein-Lazarsfeld, Ein-Lazarsfeld-Yang and gives a partial answer to some of their questions. As an application of our results, we show how to use syzygies to bound the irrationality of a variety.","authors_text":"Daniele Agostini","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-06-12T08:27:45Z","title":"Asymptotic syzygies and higher order embeddings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.03508","kind":"arxiv","version":3},"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:ee49359cf6c06e13a97cdb41311032faf10f03bac21bc582e1a9f046adeaed87","target":"record","created_at":"2026-05-18T00:16:45Z","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":"99750e540c6a129b910d181e977aa25b53e2660a60c8163bea3d936f193df100","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-06-12T08:27:45Z","title_canon_sha256":"0641c418f2b92922a35931e8eccea2e3233e2e05dd32b5d3bb12501b8de01335"},"schema_version":"1.0","source":{"id":"1706.03508","kind":"arxiv","version":3}},"canonical_sha256":"e353b418679f8f35d7e25f84fa46ce18ede209ac5014b03dc184e2746721ae40","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e353b418679f8f35d7e25f84fa46ce18ede209ac5014b03dc184e2746721ae40","first_computed_at":"2026-05-18T00:16:45.266842Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:45.266842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6WXD7OSSd6fVZGTMk4aGXuFBXWP1Ho5brWzRfWcFv22e4z6apt4wBT1OuNqVhMQNlFv0j0B9PsLJpeDWFHMLDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:45.267333Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.03508","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee49359cf6c06e13a97cdb41311032faf10f03bac21bc582e1a9f046adeaed87","sha256:ec37d798b62e1ce45e932558ccaa84deacc70780b2dc3d924540ec5adc164e4b"],"state_sha256":"1a64e2c5d709df86ca5c2342d4babb53e978e66ddc21f6e818bea1ef7e246a46"}