论文标题
Milnor纤维一致性通过平坦
Milnor Fiber Consistency via Flatness
论文作者
论文摘要
我们描述了对MILNOR纤维化的研究的一个新的代数几何观点，并且作为迈向实践的第一步，它证明了对全体形态功能胚芽变形的强大标准，可以在其领域上部分地分层，部分地满足了THOM的状况，并更普遍地满足了Milnor的原始材料，以尊重原始晶体的适当范围。作为基金会，我们获得了一种方法，可以将固定程度的均匀多项式的空间划分为有限的许多局部封闭的亚集，以使Milnor纤维的纤维差异类型沿每个子集持续不变，并且在与关键位点的函数相交的函数下面的标准下，完整的相交是良好的。
We describe a new algebro-geometric perspective on the study of the Milnor fibration and, as a first step toward putting it into practice, prove powerful criteria for a deformation of a holomorphic function germ to admit a stratification on its domain partially satisfying the Thom condition and, more generally, to respect the Milnor fibration of the original germ in an appropriate sense. As corollaries, we obtain a method of partitioning the space of homogeneous polynomials of a fixed degree into finitely many locally closed subsets such that the fiber diffeomorphism type of the Milnor fibration is constant along each subset and a criterion under which deformations of a function with critical locus a complete intersection will be well-behaved.
