{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:Z6IDFUGU522YBRIGNS3CHV6XJX","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":"4da18509bc60e167be5bca02240615b0cecc12639f982612117a97c605703db5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-04-07T13:51:11Z","title_canon_sha256":"5c1ea6d584889c160cb8391e6f435716b70cef373416e9face2ec201b0c5129b"},"schema_version":"1.0","source":{"id":"1604.01998","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.01998","created_at":"2026-05-18T01:17:31Z"},{"alias_kind":"arxiv_version","alias_value":"1604.01998v1","created_at":"2026-05-18T01:17:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.01998","created_at":"2026-05-18T01:17:31Z"},{"alias_kind":"pith_short_12","alias_value":"Z6IDFUGU522Y","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"Z6IDFUGU522YBRIG","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"Z6IDFUGU","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:a53e3616d50a0b01243609695b66e815eed88029b377e0148acc04eb94fe7b3b","target":"graph","created_at":"2026-05-18T01:17:31Z","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 this paper we construct a degeneration of Bott-Samelson-Demazure-Hansen varieties to toric varieties in an algebraic family and study the geometry of the resulting toric varieties. We give a natural set of torus invariant curves that generate the Chow group of $1$-cycles of the limiting toric variety and express the ample cone of this toric variety as a sub-cone of the ample cone of the corresponding Bott-Samelson-Demazure-Hansen variety. We also give a description of Extremal and Mori rays and determine when this toric variety is Fano.","authors_text":"A.J Parameswaran, Paramasamy Karuppuchamy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-04-07T13:51:11Z","title":"Toric Degeneration of Bott-Samelson-Demazure-Hansen varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.01998","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":"sha256:2098b50c867cae671440975a50fc99cd9e40035d2225a644ee95910bb5c78b68","target":"record","created_at":"2026-05-18T01:17:31Z","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":"4da18509bc60e167be5bca02240615b0cecc12639f982612117a97c605703db5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-04-07T13:51:11Z","title_canon_sha256":"5c1ea6d584889c160cb8391e6f435716b70cef373416e9face2ec201b0c5129b"},"schema_version":"1.0","source":{"id":"1604.01998","kind":"arxiv","version":1}},"canonical_sha256":"cf9032d0d4eeb580c5066cb623d7d74de38203c4d49779d7afea009b433d1849","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf9032d0d4eeb580c5066cb623d7d74de38203c4d49779d7afea009b433d1849","first_computed_at":"2026-05-18T01:17:31.470558Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:31.470558Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"33oNsgu+svWNpseDUTOCVkzxFYcEh3XmwItiU2/D0P1RKtvRLMoLS6CUYTgt3S+0c6y236oU4YeIB2awk576AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:31.471277Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.01998","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2098b50c867cae671440975a50fc99cd9e40035d2225a644ee95910bb5c78b68","sha256:a53e3616d50a0b01243609695b66e815eed88029b377e0148acc04eb94fe7b3b"],"state_sha256":"e7db3d999a594d761dcf2b6c4b573c7513984e8a1ba8494977359e189e719d1d"}