{"paper":{"title":"Conification of K\\\"ahler and hyper-K\\\"ahler manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.DG","authors_text":"Dmitri V. Alekseevsky, Thomas Mohaupt, Vicente Cort\\'es","submitted_at":"2012-05-14T08:56:52Z","abstract_excerpt":"Given a K\\\"ahler manifold $M$ endowed with a Hamiltonian Killing vector field $Z$, we construct a conical K\\\"ahler manifold $\\hat{M}$ such that $M$ is recovered as a K\\\"ahler quotient of $\\hat{M}$. Similarly, given a hyper-K\\\"ahler manifold $(M,g,J_1,J_2,J_3)$ endowed with a Killing vector field $Z$, Hamiltonian with respect to the K\\\"ahler form of $J_1$ and satisfying $\\mathcal{L}_ZJ_2= -2J_3$, we construct a hyper-K\\\"ahler cone $\\hat{M}$ such that $M$ is a certain hyper-K\\\"ahler quotient of $\\hat{M}$. In this way, we recover a theorem by Haydys. Our work is motivated by the problem of relati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2964","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"}