Holomorphic pre-symplectic form on the nested Hilbert scheme $Hil{b}^{3,4}({\mathbb{C}}^2)$

We regard the pre-hyperk"ahler structure on the moduli space of framed flags of sheaves $\mathcal{F}(1,3,1)$ on the projective plane ${\mathbb{P}}^2$ via an adaptation of the ADHM construction of framed sheaves. Then, we study and categorize the degenerate points of the holomorphic pre-symplectic form presented in the moduli space.