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

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