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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.

5 votes

Hitchin fibration and Springer resolution

I'll try to answer the second and third questions. My preferred way to organize this circle of ideas is to think of the following ladder of theories : Representation theory of $\mathfrak{g}$ (or) t …
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5 votes
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Bundles as Extensions and Jump Phenomena

Let $C$ be a Riemann Surface of genus $g \geq 2$. Consider a Vector Bundle of rank $r$ and degree $d$ on $C$. It is often convenient to construct such a Vector Bundle as an extension \begin{equation} …
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