Web geometry, geometry of surfaces with codimension 2 and their applications to singularity theory

1.本文研究了四维空间中余维为2的一般曲面在孤立拐点附近的渐近线的奇异性。这些奇点对应于某类二元微分方程的奇点。在这种情况下，简单奇点的类型为D1、D2、D3。也出现了更多的退化奇点，称为D23型。我们给出了D23.2型的相图。网络结构的线性化具有孤立奇点的函数的配置给出了网络结构。由此可见，奇异性理论中的有限确定性理论对于研究腹板的线性化问题是有用的。

1. Geometry of surfaces with codimension 2 in 4-spaceIn this research we have investigated singularities for the asymptotic lines of generic surfaces with codimension 2 around isolated inflection points in 4-spaces. The singularities corresponds to singularities of certain class of binary differential equations. In this case the simple singularities is of type Dl, D2, D3. Also appear more degenerated singularities, which is called type D23. We give the phase portrait of type D23.2. Linearization of web structureA configurations of functions with isolated singularities gives a web structure. It seems that a finite determined theory in singularity theory is useful to study linearization problem of webs.