{"paper":{"title":"Hamiltonian circle action with self-indexing moment map","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.SG","authors_text":"Min Kyu Kim, Yunhyung Cho","submitted_at":"2013-12-23T10:43:36Z","abstract_excerpt":"Let $(M,\\omega)$ be a $2n$-dimensional smooth compact symplectic manifold equipped with a Hamiltonian circle action with only isolated fixed points and let $\\mu : M \\rightarrow \\R$ be a corresponding moment map. Let $\\Lambda_{2k}$ be the set of all fixed points of index $2k$. In this paper, we will show that if $\\mu$ is constant on $\\Lambda_{2k}$ for each $k$, then $(M,\\omega)$ satisfies the hard Lefschetz property. In particular, if $(M,\\omega)$ admits a self-indexing moment map, i.e. $\\mu(p) = 2k$ for every $p \\in \\Lambda_{2k}$ and $k=0,1,\\cdots,n,$ then $(M,\\omega)$ satisfies the hard Lefsc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6512","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"}