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摘要翻译：
本文（B.Drinovec Drnovsek和F.Forstneric，复空间中的全纯曲线，Duke Math.J.139(2007)，203-253)得到了由强伪凸Stein域归一化的闭复子簇的存在性和逼近结果。在复流形中存在这种子簇的充分条件是用流形上耗竭函数的Morse指数和正Levi特征值的个数来表示的。实例表明，我们的条件一般不能减弱。在具有Griffiths正正规丛的紧致复子流形的补中得到了这类子簇的最优结果；在射影情形下，这些结果推广了Remmert、Bishop和Narasimhan关于真全纯映射和嵌入到复欧氏空间的经典定理。
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英文标题：
《Strongly pseudoconvex domains as subvarieties of complex manifolds》
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作者：
Barbara Drinovec Drnovsek and Franc Forstneric
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最新提交年份：
2010
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分类信息：
一级分类：Mathematics 数学
二级分类：Complex Variables 复变数
分类描述：Holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves
全纯函数，自守群作用与形式，伪凸性，复几何，解析空间，解析束
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一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
In this paper (a sequel to B. Drinovec Drnovsek and F. Forstneric, Holomorphic curves in complex spaces, Duke Math. J. 139 (2007), 203-253) we obtain existence and approximation results for closed complex subvarieties that are normalized by strongly pseudoconvex Stein domains. Our sufficient condition for the existence of such subvarieties in a complex manifold is expressed in terms of the Morse indices and the number of positive Levi eigenvalues of an exhaustion function on the manifold. Examples show that our condition cannot be weakened in general. Optimal results are obtained for subvarieties of this type in complements of compact complex submanifolds with Griffiths positive normal bundle; in the projective case these results generalize classical theorems of Remmert, Bishop and Narasimhan concerning proper holomorphic maps and embeddings to complex Euclidean spaces.
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PDF链接：
https://arxiv.org/pdf/0708.2155
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