10 problems

Let $f:(\mathbb{C}^m,0)\to(\mathbb{C}^{m+1},0)$ be an $\mathcal{A}$-finite germ in the Mather range, meaning $m\leq M(1)=14$. Its image Milnor number is denoted by $\mu_I(f)$, and…

Let $f\in\mathbb{C}[[x,y]]$ be an isolated hypersurface singularity, with Milnor number $\mu$ and Tjurina number $\tau$. Dimca–Greuel's conjecture. … The conjecture was proved comp…

In characteristic zero, let a singularity have Milnor number $\mu$, and suppose its $\mu=\mathrm{constant}$ stratum is globally singular. Stevens' conjecture. The generic member of…

Let $f\in\mathbb{C}[[x,y,z]]$ be an isolated hypersurface singularity, with Milnor number $\mu$ and Tjurina number $\tau$. Almirón's conjecture. … This is described as a weak versi…

Let $C$ be an isolated plane curve singularity, and let $bc^{k}(C)$ and $\tau^{k}(C)$ denote its $k$-th Milnor and Tjurina numbers, respectively. For every integer $k\geq 0$, Hussa…

Let $f\in\mathbb{K}[[x,y]]$ be a reduced power series, and let $\mathcal{T}$ be a minimal tree of $f$. Let $\mathcal{V}$ be the set of vertices of $\mathcal{T}$, let…

Let $g\colon(\mathbb C^3,0)\to(\mathbb C,0)$ be an augmenting function, and let $\mu(g)$ and $\tau(g)$ denote its Milnor and Tjurina numbers. The $\mu/\tau$ conjecture. It is conje…

Let $f_0$ be a map-germ from $({\mathbb C}^n,0)$ to $({\mathbb C}^{n+1},0)$, with image Milnor number $\mu_I(f_0)$ and ${\mathcal A}_e$-codimension…

Let $f_N$ be a weighted homogeneous polynomial with $1$-dimensional singularities, and let $g_j$ be the local function germs associated to the transversal singularity orbits. For w…

Let $f_t(z_0,z_1,ldots,z_n)$ be an analytic family of $n$-dimensional hypersurfaces with an isolated singularity at the origin, and suppose all these singularities have the same Mi…