多変数解析函数論3

[過去ﾛｸﾞ] 多変数解析函数論3 (1002ﾚｽ)
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101: １３２人目の素数さん [] 2024/01/05(金) 17:25:18.17 ID:U1/CtORy

>>92
>[127]は学位論文で
>修論の結果を当時としては最大限に一般化したものだったが
>それではまだ不十分だったということで

なるほど、私には お経ですがPDF貼ります
[127] T.Ohsawa, Isomorphismtheorems for cohomology groups of weakly 1complete manifolds,Publ.Res. Inst.Math.Sci.KyotoUniv. 18(1982)
https://ems.press/journals/prims/articles/3041
https://ems.press/content/serial-article-files/3073
Table of Contents
Chapter 1 Preliminaries 193
§1 Hermitian geometry 193
§2 Lz estimates of d 197
Chapter 2 Isomorphism theorems for pseudo-Runge pairs 200
§1 Basic estimates 200
§2 Pseudo-Runge pairs and an approximation theorem 201
§3 Isomorphism theorems 204
§4 Examples of pseudo-Runge pairs 207
Chapter 3 Isomorphism theorems on weakly 1-complete manifolds 214
§1 Coarse isomorphism theorems 214
§2 Precise isomorphism theorems 218
Appendix 225

Introduction
In the theory of complex manifolds, there are two different extreme objects:
compact manifolds and holomorphically complete ones. We have a lot of good
knowledge about the fundamental properties of both classes of manifolds, contributions to which have been made by many celebrated authors in this century.
In 1970, S. Nakano [18] succeeded in solving a problem on the inverse of
monoidal transformation by proving the vanishing of cohomology groups for
line bundles over a class of complex manifolds. This class includes the above
extremes and was called by him weakly 1-complete manifolds. The definition
is as follows; a complex manifold is said to be weakly 1-complete if it carries a
C°° plurisubharmonic exhaustion function. It is trivial that a compact complex
manifold is weakly 1-complete. It follows immediately from the Remmert's
proper embedding theorem that holomorphically complete manifolds are weakly 1-complete.
From the definition, it is quite natural to expect that a weakly 1-complete
manifold is a nice intermediate object between compact complex manifolds and holomorphically complete ones.
In the last decade, more or less inspired by this philosophy, several authors
have studied cohomological properties of weakly 1 -complete manifolds: [1],
[12], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29]. The following theorem is due to S. Nakano [21].

The author expresses his hearty thanks to Professor S. Nakano who led him
to this subject. He is also very grateful to Professor H. Grauert who allowed
him to stay in Gottingen during the preparation of this paper and gave him kind
advices. Last but not least he expresses many thanks to Mr. K. Takegoshi for
careful reading of the manuscript and to the referee for valuable criticisms.

http://rio2016.5ch.net/test/read.cgi/math/1701572410/101

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