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I would like to know if people have constructed an algebro-geometric description or interpretation of the ramified Donaldson invariants of Kronheimer and Mrowka in the same spirit of Li, see for example here.

The ramified Donaldson invariants are defined for smooth four-manifolds $X$ with an embedded complex surface $S$. Then the ramified Donaldson invariants are defined in terms of a the moduli space $M$ of ramified instantons defined over $X \backslash S$. For more details see the first reference but roughly they are integrals of differential forms over $M$.

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