13 problems

Let a family of singularities have constant Milnor number, denoted by $\mu$; Whitney conditions are the usual geometric regularity conditions for the family. Teissier's conjecture.…

Let $X_t$ be a family of hypersurfaces in $\mathbb{C}^3$ parameterized by finitely determined map germs $f_t$, and let $D(f_t)$ denote the double point curve of $f_t$. Ruas' conjec…

Whitney's fibering conjecture. Every analytic subvariety $V\subset U$ has a stratification such that each point $p_0\in V$ has a neighborhood $U_0$ with a semi-analytic fibration.

Let $(V(f),\0) \subseteq ({\mathbb C}^3,\0)$ be a reduced hypersurface with $\dim_\0 \Sigma f=1$, and suppose that the normalization of $V(f)$ is a bijection. Lê's conjecture. Then…

Conjecture C. $f$ is a function germ with smooth $1$-dimensional critical set such that the transversal Milnor number of $f$ at every point of its critical set is equal to $\mu$.

Conjecture B. Any function germ $g$ topologically equisingular to $f$ has smooth critical set and constant transversal Milnor number.

Conjecture A. The family $f_t$ is equisingular at the critical set if and only if $f_t$ is topologically equisingular to $f_{t'}$ for any parameters $t,t'$.

Let $Y$ be a complex analytic manifold and let $f:Y\to\Delta$ be a projective morphism, where $\Delta$ is a disc. A morphism is a homotopy fiber bundle if it has the homotopy-local…

Let a family of hypersurface singularities have constant Milnor number $\mu$, and let multiplicity denote the multiplicity of the hypersurface singularity at the relevant point. Te…

Let $X \subset \mathbb{C}^{n+k}$ be an equidimensional complex analytic space, let $Y$ be a smooth subspace of $X$ of dimension $k$, and suppose that $X-Y$ is smooth. Let…

Teissier's conjecture. Invariance of the Milnor number in the family should imply invariance of all sectional Milnor numbers, equivalently invariance of $\mu^*$. This conjecture wa…

Let $(X,x)$ be a surface singularity, let $f:(X,x)\to(\mathbb C,0)$ be flat with $(X_0,x)=(f^{-1}(0),x)$ an isolated curve singularity, and let $f:X\to T$ be a good representative…

Excellence conjecture. If $\mu_I$ is constant, then the unfolding is excellent.