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Let $w$ be an element of the Weyl group $W$ of $G$, and let $Z(\\tilde w)$ be the Bott-Samelson-Demazure-Hansen (BSDH) variety corresponding to a reduced expression $\\tilde w$ of $w$ with respect to the data $(G, B, T)$. In this article we give complete characterization of the expressions $\\tilde w$ such that the corresponding BSDH variety $Z(\\tilde w)$ is Fano or weak Fano. As a consequence we prove vanishing theorems of the cohomology of tangent bundle"},"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":"1801.07510","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-01-23T12:33:02Z","cross_cats_sorted":[],"title_canon_sha256":"55e9e2368d7353ec7d829a0657af7a7f80122fc8b5515e08bbd6e4f4376fbbdd","abstract_canon_sha256":"221a0c455243a562430d4d987ad129e301fa34ce9c268a15419d64074d617999"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:00.208965Z","signature_b64":"PwhH7GdnO2pAVeqAbOcKUkARu5e7RLCc9kY9VD94+6J/HRKcOEtfw1kvPalOlayHcuNJeM5urDKX1pmS1vOoBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f0f592e9be45ffe2527948b4571e4ad54ef7173162be45f209cc04f5574c889","last_reissued_at":"2026-05-18T00:09:00.208338Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:00.208338Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Fano and weak Fano Bott-Samelson-Demazure-Hansen varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"B. 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