>>84-86 もどる 補足

(参考)
https://projecteuclid.org/journalArticle/Download?urlId=10.1007%2Fs11512-008-0084-y
Ark. Mat., 48 (2010), 207–210
A long C2 which is not Stein Erlend Fornæss Wold
Abstract. We construct a 2-dimensional complex manifold X which is the increasing union of proper subdomains that are biholomorphic to C2, but X is not Stein.

https://arxiv.org/abs/1511.05075
https://arxiv.org/pdf/1511.05075
[Submitted on 16 Nov 2015 (v1), last revised 29 Aug 2016 (this version, v4)]
A long C without holomorphic functions
Luka Boc Thaler, Franc Forstneric
Abstract
In this paper we construct for every integer a complex manifold of dimension which is exhausted by an increasing sequence of biholomorphic images of C (i.e., a long C), but it does not admit any nonconstant holomorphic or plurisubharmonic functions. Furthermore, we introduce new biholomorphic invariants of a complex manifold , the stable core and the strongly stable core, that are based on the long term behavior of hulls of compact sets with respect to an exhaustion of . We show that every compact polynomially convex set C which is the closure of its interior is the strongly stable core of a long C; in particular, biholomorphically nonequivalent sets give rise to nonequivalent long C's. Furthermore, for any open set C there exists a long C whose stable core is dense in . It follows that for any there is a continuum of pairwise nonequivalent long C's with no nonconstant plurisubharmonic functions and no nontrivial holomorphic automorphisms. These results answer several long standing open problems.