{"paper":{"title":"Classification of six dimensional monotone symplectic manifolds admitting semifree circle actions I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Yunhyung Cho","submitted_at":"2018-12-24T11:22:31Z","abstract_excerpt":"Let $(M,\\omega_M)$ be a six dimensional closed monotone symplectic manifold admitting an effective semifree Hamiltonian $S^1$-action. We show that if the minimal (or maximal) fixed component of the action is an isolated point, then $(M,\\omega_M)$ is $S^1$-equivariant symplectomorphic to some K\\\"{a}hler Fano manifold $(X,\\omega_X, J)$ with a certain holomorphic $\\mathbb{C}^*$-action. We also give a complete list of all such Fano manifolds and describe all semifree $\\mathbb{C}^*$-actions on them specifically."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.09892","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"}