13 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 $X_t$ 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…

Let $f\colon(\mathbb{C}^n,0)\to(\mathbb{C}^p,0)$ be an $\mathcal{A}$-finite map-germ whose stable unfolding with the minimal number of parameters lies in the nice dimensions. A sta…

Let $f:(\mathbb{C}^n,0)\rightarrow (\mathbb{C}^{2n},0)$ be an $\mathcal{A}$-finite map germ. Suppose that $f$ is quasihomogeneous of type $(w_1,\ldots,w_n;d_1,\ldots,d_{2n})$, wher…

Consider corank $1$ simple augmentations of map-germs from $\mathbb C^4$ to $\mathbb C^4$. The classification conjecture. All such augmentations are the ones given in Table of the…

Let $f\colon (\mathbb{C}^n,0)\to(\mathbb{C}^{n+1},0)$ be a stable proper frontal map germ of corank $1$, with Legendrian lift $\tilde f$. Define Ishikawa's indices by … Here square…

No coalescence conjecture. The coalescence problem does not occur: a one-parameter deformation $f_t$ cannot have more than one instability and satisfy

Contractible stable perturbation conjecture. There are such germs for which

An augmentation is the construction discussed in the paper that produces a map-germ from a map-germ and an augmenting function. The paper lists certain simple augmentations from…

Boundary extra-nice-dimensions conjecture. Any two generic immersions $g$ and $g'$ are bi-Lipschitz $\mathcal{K}_{V}$-equivalent, and the germs $f$ and $f'$ they define are bi-Lips…

Let $f$ be the map-germ considered in the paper, and let a stable perturbation of $f$ have quadruple points. Quadruple-point count conjecture. The number of quadruple points is…

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 $\varphi_1,\varphi_2:(\mathbb{R}^2,0)\to(\mathbb{R}^3,0)$ be two $C^\infty$ map-germs of pedal unfolding type. Let $\Phi_1,\Phi_2:(\mathbb{R}^2,0)\to(\mathbb{R}^3,0)$ be two no…