{"paper":{"title":"A sm\\\"org\\r{a}sbord of scalar-flat K\\\"ahler ALE surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jeff A. Viaclovsky, Michael T. Lock","submitted_at":"2014-10-23T19:28:17Z","abstract_excerpt":"There are many known examples of scalar-flat K\\\"ahler ALE surfaces, all of which have group at infinity either cyclic or contained in ${\\rm{SU}}(2)$. The main result in this paper shows that for any non-cyclic finite subgroup $\\Gamma \\subset {\\rm{U}}(2)$ containing no complex reflections, there exist scalar-flat K\\\"ahler ALE metrics on the minimal resolution of $\\mathbb{C}^2 / \\Gamma$, for which $\\Gamma$ occurs as the group at infinity. Furthermore, we show that these metrics admit a holomorphic isometric circle action. It is also shown that there exist scalar-flat K\\\"ahler ALE metrics with re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6461","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"}