Kähler compactification of Cn and Reeb dynamics

• 成果类型: Article; Early Access
• 署名作者: Li, Chi; Zhou, Zhengyi
• 署名单位: Rutgers University System; Rutgers University New Brunswick; Chinese Academy of Sciences; Chinese Academy of Sciences; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-025-01377-2
• 发表日期: 2025
• 关键词: analytic compactifications; exact sequence; MANIFOLDS; HOMOLOGY; contact

摘要

Let X be a smooth complex manifold. Assume that Y subset of X is a K & auml;hler submanifold such that X\Y is biholomorphic to Cn. We prove that (X,Y) is biholomorphic to (Pn,Pn-1). We then study certain K & auml;hler orbifold compactifications of Cn and, as an application, prove that on C3 the flat metric is the only asymptotically conical Ricci-flat K & auml;hler metric whose metric cone at infinity has a smooth link. As a key technical ingredient, we derive a new characterization of minimal discrepancy of isolated Fano cone singularities by using S1-equivariant positive symplectic homology.