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Okay, I cannot give you a full understanding of what is going on, but I can make the objects we are dealing with more precise: There are two spaces here: The moduli space $M_\text{sh}(r,k)$ of framed torsion-free coherent sheaves of rank $r$ and second Chern class $k$ on the projective scheme $\mathbb{P}^2$ viewed as a complex analytic space with its ...

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