标题： 拟齐次性的向可提升向量场刻画 显示英文标题

标题： A characterization of quasi-homogeneity in terms of liftable vector fields

摘要： 我们在某些条件下证明，拟齐次映射芽具有有限奇点类型时，其任意稳定的延展都是实质性的。 接着我们证明，若一个同维数的映射芽是有限决定的，余秩为 1，并且要么它有一个极小稳定延展，要么它的多重度为 3，则它具有实质性延展当且仅当它是拟齐次的。 基于此，我们提出如下猜想：有限决定的映射芽是拟齐次的当且仅当它具有实质性延展。 显示英文摘要

摘要： We prove under certain conditions that any stable unfolding of a quasi-homogeneous map-germ with finite singularity type is substantial. We then prove that if an equidimensional map-germ is finitely determined, of corank 1, and either it admits a minimal stable unfolding or it is of multipliticy 3, then it admits a substantial unfolding if and only if it is quasi-homogeneous. Based on this we pose the following conjecture: a finitely determined map-germ is quasi-homogeneous if and only if it admits a substantial unfolding.