3 problems

Houston's conjecture. Excellency in families can be controlled by means of the image Milnor number.

Let $f\colon(\mathbb{C}^{n},S)\rightarrow(\mathbb{C}^{n+1},0)$ be an $\mathscr{A}$-finite germ, and let $F(x,t)=(f_t(x),t)$ be an origin-preserving one-parameter unfolding. The exc…

Let $F(x,t)=(f_t(x),t)$ be an origin-preserving one-parameter unfolding. The unfolding is excellent if it admits a stratification by stable types such that the parameter axes are t…