{"paper":{"title":"Unstable points for torus actions on flag varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Beno\\^it Dejoncheere","submitted_at":"2017-09-18T13:56:36Z","abstract_excerpt":"In this paper, we will look at actions on complex flag varieties $G/P$ of the torus $\\hat{T}=\\bigcap\\limits_{\\alpha\\in\\Delta\\setminus\\Delta_P}\\ker(\\alpha)$, and under reasonable assumptions, we will give a description of the set $X^{us}$ of unstable points for $\\hat{T}$-linearized invertible sheaves. We will investigate the case where $P$ is a maximal parabolic subgroup, and show that $X^{us}$ can be written as a disjoint union of a Schubert variety and an opposite Schubert variety, and we deduce the vanishing of cohomology groups $H^i(Y,{\\cal M})$ for invertible sheaves ${\\cal M}$ on the quot"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.05942","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"}