Function theoretic properties of symmetric powers of complex manifolds

2018/04/25 by Włodzimierz Zwonek, Zwonek, Włodzimierz
Mathematics · #32C15 #32F45 #32T40 #Complex Variables (math.CV) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1804.09600

openalex publication_date 2018/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the paper we study properties of symmetric powers of complex manifolds. We investigate a number of function theoretic properties (e. g. (quasi) c-finite compactness, existence of peak functions) that are preserved by taking the symmetric power. The case of symmetric products of planar domains is studied in a more detailed way. In particular, a complete description of the Carathéodory and Kobayashi hyperbolicity and Kobayashi completeness in that class of domains is presented.

Related

• Hyperbolicity and Specialness of Symmetric Powers
• Holomorphic symmetric differentials and parallelizable compact complex manifolds
• Function theory and holomorphic maps on symmetric products of planar\n domains
• Algebroid maps and hyperbolicity of symmetric powers
• Symmetric Products and Q-manifolds