  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.
