{"paper":{"title":"Ergodic complex structures on hyperkahler manifolds","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.CV","math.DG"],"primary_cat":"math.AG","authors_text":"Misha Verbitsky","submitted_at":"2013-06-06T18:27:31Z","abstract_excerpt":"Let $M$ be a compact complex manifold. The corresponding Teichmuller space $\\Teich$ is a space of all complex structures on $M$ up to the action of the group of isotopies. The group $\\Gamma$ of connected components of the diffeomorphism group (known as the mapping class group) acts on $\\Teich$ in a natural way. An ergodic complex structure is the one with a $\\Gamma$-orbit dense in $\\Teich$. Let $M$ be a complex torus of complex dimension $\\geq 2$ or a hyperkahler manifold with $b_2>3$. We prove that $M$ is ergodic, unless $M$ has maximal Picard rank (there is a countable number of such $M$). T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1498","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"}