{"paper":{"title":"Pseudoconcavity of flag domains: The method of supporting cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"A. Huckleberry, Q. Latif, T. Hayama","submitted_at":"2017-11-26T04:19:20Z","abstract_excerpt":"A flag domain of a real from $G_0$ of a complex semismiple Lie group $G$ is an open $G_0$-orbit $D$ in a (compact) $G$-flag manifold. In the usual way one reduces to the case where $G_0$ is simple. It is known that if $D$ possesses non-constant holomorphic functions, then it is the product of a compact flag manifold and a Hermitian symmetric bounded domain. This pseudoconvex case is rare in the geography of flag domains. Here it is shown that otherwise, i.e., when $\\mathcal{O}(D)\\cong\\mathbb{C}$, the flag domain $D$ is pseudoconcave. In a rather general setting the degree of the pseudoconcavit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.09333","kind":"arxiv","version":2},"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"}