3 problems

Let $r$ and $k$ be positive integers, and let $I^{2r+1,k}_r$ denote the jet pfaffian ideal associated with the ideal of size-$2r$ pfaffians of a generic $(2r+1)\times(2r+1)$ skew-s…

Sullivant's conjecture. For every $r$, one has

Let $J=\operatorname{Pf}_4({\mathbf X})+I_1({\mathbf t}{\mathbf X})$, where ${\mathbf X}$ is a generic alternating matrix and ${\mathbf t}$ is a generic row vector. Here…