3 problems

Equality conjecture.

Let $K$ be the ground field, let $R=K[[x_1,\ldots,x_s]]$ with maximal ideal $\mathfrak{m}$, and let $A\in\mathfrak{m}\cdot M_{m,n}$ be a matrix. Let $G$ act on $M_{m,n}$ by the equ…

Let $f_0$ be a generic corank $1$ matrix singularity for an $m \times m$ symmetric, general, or, when $m$ is even, skew-symmetric matrix. Let $\mathcal{D}$ be the corresponding det…