{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:6MG4GQ3JHFBEPIPQXHXDQS5XBQ","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":"844c75d15244a2823b930a2c0b91e52663cf0607c0698142b4fce13426b9e2d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-06-07T02:41:11Z","title_canon_sha256":"d68fbe78c7174c0648f0d29ea17bfae4d7a532f69e6d7c8247040a04cf97ac13"},"schema_version":"1.0","source":{"id":"1706.02032","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.02032","created_at":"2026-05-18T00:31:55Z"},{"alias_kind":"arxiv_version","alias_value":"1706.02032v1","created_at":"2026-05-18T00:31:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.02032","created_at":"2026-05-18T00:31:55Z"},{"alias_kind":"pith_short_12","alias_value":"6MG4GQ3JHFBE","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6MG4GQ3JHFBEPIPQ","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6MG4GQ3J","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:6693920a5b72b353456c95c0f4f81d5dae9c1020b6e399aa8271c8e447ffc993","target":"graph","created_at":"2026-05-18T00:31:55Z","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":"For $m\\geq n$, Let $K$ be an algebraic closed base field, and define $\\tau_{m,n,k}$ to be the set of $m\\times n$ matrices over $K$ with kernel dimension $\\geq k$. This is a projective subvariety of $\\mathbb{P}^{mn-1}$, and is usually called determinantal variety. In most cases $\\tau_{m,n,k}$ is singular with singular locus $\\tau_{m,n,k+1}$. In this paper we compute the local Euler obstruction of $\\tau_{m,n,k}$, and we prove that the characteristic cycle of the intersection cohomology complex of $\\tau_{m,n,k}$ is irreducible. We also give an explicit formula for the Chern-Mather class of $\\tau_","authors_text":"Xiping Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-06-07T02:41:11Z","title":"Local Euler Obstruction and Chern-Mather classes of Determinantal Varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02032","kind":"arxiv","version":1},"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":"sha256:856b77a8cf38c91110de673765c3359053e452efa304a4e9d6c6b9ef09c8ec9d","target":"record","created_at":"2026-05-18T00:31:55Z","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":"844c75d15244a2823b930a2c0b91e52663cf0607c0698142b4fce13426b9e2d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-06-07T02:41:11Z","title_canon_sha256":"d68fbe78c7174c0648f0d29ea17bfae4d7a532f69e6d7c8247040a04cf97ac13"},"schema_version":"1.0","source":{"id":"1706.02032","kind":"arxiv","version":1}},"canonical_sha256":"f30dc34369394247a1f0b9ee384bb70c156329dcf4e5a28a955c3d11ec024c3d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f30dc34369394247a1f0b9ee384bb70c156329dcf4e5a28a955c3d11ec024c3d","first_computed_at":"2026-05-18T00:31:55.825495Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:55.825495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L32vKLImUURxJ2kK7moMYv6ktPiAPfq6CWhg5r6BvwSE38KrdSnThRBNaQwTvyIPXF+9bPqSEJlcv9HknUpRCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:55.825986Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.02032","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:856b77a8cf38c91110de673765c3359053e452efa304a4e9d6c6b9ef09c8ec9d","sha256:6693920a5b72b353456c95c0f4f81d5dae9c1020b6e399aa8271c8e447ffc993"],"state_sha256":"4b130a0b3138af599d526ab7acc8eefb49b160a8efaa844a8891ff1ccde12d97"}