Ergodic complex structures on hyperkahler manifolds

• 成果类型: Article
• 署名作者: Verbitsky, Misha
• 署名单位: HSE University (National Research University Higher School of Economics); University of Tokyo
• 刊物名称: ACTA MATHEMATICA
• ISSN/ISSBN: 0001-5962
• DOI: 10.1007/s11511-015-0131-z
• 发表日期: 2015
• 页码: 161-182
• 关键词: kahler-manifolds; homogeneous spaces; twistor spaces; HYPERBOLICITY; VARIETIES; torelli; METRICS; FLOWS; cone

摘要

Let M be a compact complex manifold. The corresponding Teichmuller space Teich is the space of all complex structures on M up to the action of the group of isotopies. The mapping class group acts on Teich in a natural way. An ergodic complex structure is a complex structure with a -orbit dense in Teich. Let M be a complex torus of complex dimension or a hyperkahler manifold with . We prove that M is ergodic, unless M has maximal Picard rank (there are countably many such M). This is used to show that all hyperkahler manifolds are Kobayashi non-hyperbolic.