{"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. Narasimha Chary","submitted_at":"2018-01-23T12:33:02Z","abstract_excerpt":"Let $G$ be a simple algebraic group over the field of complex numbers. Fix a maximal torus $T$ and a Borel subgroup $B$ of $G$ containing $T$. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.07510","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}