论文标题
关于一个变量中向量领域的普遍展开：科斯托夫定理的证明
On the universal unfolding of vector fields in one variable: A proof of Kostov's theorem
论文作者
论文摘要
在本说明中，我们介绍了Kostov定理的变体，内容涉及复杂分析$ 1 $维矢量字段的抛物线点的多种变形。首先，我们提供了科斯托夫定理的独立证明，并证明这种广泛的变形确实是普遍的。然后，我们将表现出普遍性的真实分析和正式案例概括为$ c^\ infty $案例，在那里我们表明只有广义性是可能的。
In this note we present variants of Kostov's theorem on a versal deformation of a parabolic point of a complex analytic $1$-dimensional vector field. First we provide a self-contained proof of Kostov's theorem, together with a proof that this versal deformation is indeed universal. We then generalize to the real analytic and formal cases, where we show universality, and to the $C^\infty$ case, where we show that only versality is possible.
