关于平面分支极线的因式分解
On the factorization of the polar of a plane branch
摘要：
本文给出了复平面曲线不可约芽的等奇异类的一般成员的一般极线的因式分解的尽可能完整的描述。我们的结果将改进M. Merle在70年代提出的，它是基于E. Casas-Alvero在90年代描述了这种极的奇点簇。利用我们的分析，将有可能刻画具有r个特征指数的不可约平面芽的所有等奇异类，这些类具有特殊的行为，即在这个等奇异类中一般曲线的一般极线只具有小于r个特征指数的不可约分量，推广了作者以前在r=2时得到的结果。
英文摘要：
In this paper we present the most complete description as possible of the factorization of the general polar of the general member of an equisingularity class of irreducible germs of complex plane curves. Our result will refine the rough description of the factorization given by M. Merle in the 70's and it is based on a result given by E. Casas-Alvero in the 90's that describes the cluster of the singularities of such polars. By using our analysis, it will be possible to characterize all equisingularity classes of irreducible plane germs with r characteristic exponents having the exceptional behavior that the general polar of a general curve in this equisingularity class has only irreducible components with less than r characteristic exponents, generalizing a result previously obtained for r=2 by the authors.
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