Function theoretic properties of symmetric powers of complex manifolds

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.

13 pages

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