Singularity of Quot schemes containing twisted cotangent bundles

Prove or disprove that the Quot schemes containing a point corresponding to the twisted cotangent bundle \(\Omega_{\mathbb{P}^{n}}(2)\) are singular for every \(n\geq 3\).

Background

The paper gives an explicit example for $n=3$ in which the Quot scheme containing the twisted cotangent bundle $\Omega_{\mathbb{P}^{3}}(2)$ is singular. It then discusses computational data for dimensions up to $n=9$.

The observed multiplicities grow rapidly and lead the authors to formulate the all-dimensional assertion only as an apparent pattern; the statement remains unresolved for general $n\geq 3$.