论文标题
平面分支和奇异叶的分析半摩托
Analytic semiroots for plane branches and singular foliations
论文作者
论文摘要
方程平面分支的分析模量具有差分值的半模块，作为最相关的离散不变系统。集中在尖端的情况下，该半模块的发电机的最小系统由所谓的标准基础的微分$ 1 $形式的差异值达到了。我们可以通过添加最后一个差异$ 1 $形式来完成标准基础，该差额为不变分支和``正确''分区订单。这种扩大的标准碱基的元素具有``cuspidal''除数为``完全双向分裂''，因此它们定义了平面分支的包装，这些套件是在最初的一部分。这些是分析性半摩托。在本文中，我们证明，从几何和叶状的观点中，扩大的标准底座是很好的结构，因为在某种意义上，在相应的差异值处，dicricition包装中分支差异值的半模块仅通过对初始半模块的发电机列表的截断来描述。特别是它们具有差分值的所有相同半模块。
The analytic moduli of equisingular plane branches has the semimodule of differential values as the most relevant system of discrete invariants. Focusing in the case of cusps, the minimal system of generators of this semimodule is reached by the differential values attached to the differential $1$-forms of the so-called standard bases. We can complete a standard basis to an enlarged one by adding a last differential $1$-form that has the considered cusp as invariant branch and the ``correct'' divisorial order. The elements of such enlarged standard bases have the ``cuspidal'' divisor as a ``totally dicritical divisor'' and hence they define packages of plane branches that are equisingular to the initial one. These are the analytic semiroots. In this paper we prove that the enlarged standard bases are well structured from this geometrical and foliated viewpoint, in the sense that the semimodules of differential values of the branches in the dicritical packages are described just by a truncation of the list of generators of the initial semimodule at the corresponding differential value. In particular they have all the same semimodule of differential values.
