4 problems

Let $\mathcal{T}^n_{d,e,m}$ denote the Taylor variety, and call it defective when its dimension is smaller than the expected dimension. Defectivity conjecture. The following statem…

Let $H_f$ be the Hessian matrix of the determinant $f=\det(P_T)$ of the Padé matrix in the cases covered by the vanishing-Hessian discussion, and let the generic corank mean the di…

For integers $d,e$ with $(d,e)\geq(1,2)$, let $\mathcal{T}^1_{d,e,d+e+1}$ be the Taylor variety associated with univariate rational functions of numerator degree $d$ and denominato…

Let $P_T$ be the Padé matrix defining the Taylor variety $\mathcal{T}^n_{d,e,m}$, let $\hat P_T$ be the matrix obtained from $P_T$ by deleting its leftmost column, and let…