Maximally tangent complex curves for germs of finite type $${\mathcal{C}^\infty}$$ pseudoconvex domains in $${\mathbb C^3}$$
Maximally tangent complex curves for germs of finite type $${\mathcal{C}^\infty}$$ pseudoconvex domains in $${\mathbb C^3}$$
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有限类型细菌的最大正切复曲线 $${mathcal{C}^infty}$$ 伪凸域 $${mathbb C^3}$$
DOI：
10.1007/s00208-009-0462-1
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
Berit Stensønes
中科院分区：
文献类型：
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作者：
J. Fornæss;Berit Stensønes
本文讨论了D 'Angelo有限型拟凸域Ω在.我们感兴趣的是与高阶相切的复曲线。我们的主要结果是，只有100多条曲线的极大型。最大类型必须在微局部意义上进行，因为最大类型在不同方向上可以不同。当然，为了得到有限性，我们必须忽略高阶无关项，因为它们可以不受限制地相加。在描述这样的曲线的过程中，我们发现坐标的奇异变化将曲线简化为复杂的直线。
In this paper we discuss D’Angelo finite type pseudoconvex domains Ω in. We are interested in complex curves tangent to higher order. Our main result is that there are only finitely many curves of maximal type. Maximal type has to be taken in a micro-local sense since the maximal type can be different in different directions. And of course to get finiteness we have to ignore higher order irrelevant terms which can be added without restriction. In the process of describing such a curve we find a singular change of coordinates which reduces the curve to a complex line.