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Given a concrete category C, with objects denoted Obj(C), and an equivalence relation ~ on Obj(C) given by morphisms in C. The moduli set for Obj(C) is the set of equivalence classes with respect to ~; denoted Iso(C). When Iso(C) is an object in the category Top, then the moduli set is called a moduli space.

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Stable torsion free sheaf on smooth projective surface

The above statement on surfaces is correct if you suppose $E$ to be locally free, otherwise you should pay attention to torsion free subsheaves as well. I am thinking about the direct sum $E = I_p \op …
Oscar Amalfitano's user avatar