Every Stein subvariety admits a Stein neighborhood
Every Stein subvariety admits a Stein neighborhood
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每个斯坦因子品种都承认一个斯坦因邻域
DOI：
10.1007/bf01390170
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发表时间：
1976
影响因子：
3.1
通讯作者：
Y. Siu
中科院分区：
文献类型：
--
作者：
Y. Siu
Douady[11，附录]和LeBarz[3]给出了主定理的一些特殊情况。Douady证明了X是Stein空间Y的一个相对紧的开子集，且对于Y的某个子变种V， a = Xc~ V的特殊情况。LeBarz证明了a和X都是非奇异的特殊情况，并证明了X中a的某个开邻域的切束允许全纯连接或由全局全纯截面生成。我们的证明方法使用Richberg的结果[7]和Grauert[2]发明的技术来证明具有弱负广义正规束的紧子变体是例外的，并使用了考虑某Reinhardt域的全纯包络而产生的一个特殊的多次调和函数。然后明确构造所需的Stein邻域，并通过生成连续严格多次谐波耗尽函数和引用Narasimhan的结果[4]证明其斯坦性。主要定理有以下三个直接的推论。
Some special cases of the Main Theorem were obtained by Douady [11, Appendice] and LeBarz [3]. Douady proved the special case where X is a relatively compact open subset of a Stein space Y and A= Xc~ V for some subvariety V of Y. LeBarz proved the special case where A and X are both nonsingular with the additional property that the tangent bundle of some open neighborhood of A in X admits a holomorphic connection or is generated by global holomorphic cross sections.Our method of proof uses Richberg's result [7] and the techniques which Grauert [2] devised to prove that a compact subvariety with a weakly negative generalized normal bundle is exceptional and uses a special plurisubharmonic function which arises from considering the envelope of holomorphy of a certain Reinhardt domain. The required Stein neighborhood is then explicitly constructed and its Steinness is proved by producing a continuous strictly plurisubharmonic exhaustion function and invoking Narasimhan's result [4]. The Main Theorem has the following three corollaries as immediate consequences.