9 problems

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…

Mond conjecture.

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

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 $f:(\mathbb{C}^2,0)\rightarrow(\mathbb{C}^3,0)$ be a finitely determined map germ, and let $F:(\mathbb{C}^2\times\mathbb{C},0)\rightarrow(\mathbb{C}^3\times\mathbb{C},0)$ be a…

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…