{"paper":{"title":"Counterexamples to hyperkahler Kirwan surjectivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Kevin McGerty, Thomas Nevins","submitted_at":"2019-04-26T18:08:03Z","abstract_excerpt":"Suppose that M is a complete hyperkahler manifold with a compact Lie group K acting via hyperkahler isometries and with hyperkahler moment map $(\\mu_{\\mathbb{C}}, \\mu_{\\mathbb{R}}): M\\rightarrow \\mathfrak{k}^*\\otimes\\operatorname{Im}(\\mathbb{H})$. It is a long-standing problem to determine when the hyperkahler Kirwan map $H^*_K(M,\\mathbb{Q}) \\longrightarrow H^*(M//K, \\mathbb{Q})$ is surjective. We show that for each $n\\geq 2$, the natural $U(n)$-action on $M = T^*(SL_n\\times\\mathbb{C}^n)$ admits a hyperkahler quotient for which the hyperkahler Kirwan map fails to be surjective. As a tool, we e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.12003","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"}