{"paper":{"title":"Ergodic complex structures on hyperkahler manifolds: an erratum","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CV","math.DS"],"primary_cat":"math.AG","authors_text":"Misha Verbitsky","submitted_at":"2017-08-19T03:53:07Z","abstract_excerpt":"Let $M$ be a hyperkahler manifold, $\\Gamma$ its mapping class group, and $Teich$ the Teichmuller space of complex structures of hyperkahler type. After we glue together birationally equivalent points, we obtain the so-called birational Teichmuller space $Teich_b$. Every connected component of $Teich_b$ is identified with its period space $P$ by global Torelli theorem. The mapping class group of $M$ acts on $P$ as a finite index subgroup of the group of isometries of the integer cohomology lattice, that is, satisfies assumptions of Ratner theorem. We prove that there are three classes of orbits"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.05802","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"}