{"paper":{"title":"$G$-minimality and invariant negative spheres in $G$-Hirzebruch surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Weimin Chen","submitted_at":"2013-12-03T15:19:41Z","abstract_excerpt":"In this paper a study of $G$-minimality, i.e., minimality of four-manifolds equipped with an action of a finite group $G$, is initiated. We focus on cyclic actions on $CP^2\\# \\overline{CP^2}$, and our work shows that even in this simple setting, the comparison of $G$-minimality in the various categories, i.e., locally linear, smooth, and symplectic, is already delicate and interesting. For example, we show that if a symplectic $Z_n$-action on $CP^2\\# \\overline{CP^2}$ has an invariant locally linear topological $(-1)$-sphere, then it must admit an invariant symplectic $(-1)$-sphere, provided th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0848","kind":"arxiv","version":3},"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"}