ガロア第一論文と乗数イデアル他関連資料スレ5

[過去ﾛｸﾞ] ガロア第一論文と乗数イデアル他関連資料スレ5 (1002ﾚｽ)
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728: １３２人目の素数さん [] 2023/07/17(月) 06:30:33.35 ID:GpeoaFRE

\textbf{Remark.}    As was noted in [C-D], $\hat{\Omega}$ is a ramified locally pseudoconvex
Riemann domain over $\mathbb{C}^3$ whose fiber are separable by holomorphic functions
by a theorem of Siu in [S]. Hence, as a complex manifold, $\hat{\Omega}$ is embeddable into
$\mathbb{C}^N$ as a locally closed complex analytic submanifold.  Since this submanifold is locally
Stein, it amounts to a counterexample of a question raised by P.A. Griffiths in 1977 in Kyoto.
However, it is still an open question whether or not the locally pseudoconvex ramified Riemann domain
constructed by Fornaess [F] is embeddable into some $\mathbb{C}^N$ as a locally closed submanifold.
It may be worthwhile to note that Proposition 1 implies that the manifold $\hat{F}$ can be realized as
a ramified Riemann domain, by virtue of the $L^2$ theory of Demailly [Dm] (see also [Oh-1]),
since the canonical bundle of $\hat{F}$ is trivial. It is likely that one can construct holomorphic functions
on $\hat{F}$
holomorphic functions more explicitly as (2).

http://rio2016.5ch.net/test/read.cgi/math/1687778456/728

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