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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.

16 votes

Is a 'generic' variety nonsingular? Or singular?

Here are some elementary remarks which would lead me to bet that a variety, of which I am told nothing, is nonsingular. I want to emphasize that I am not answering your question very satisfactorily ( …
Georges Elencwajg's user avatar
15 votes

Reference request: moduli spaces of vector bundles

Dear Mohammad, there is a rather elementary book Introduction to Moduli Problems and Orbit spaces by P.E. Newstead which will explain to you why stability is important, give you lots of examples (Ch …
Georges Elencwajg's user avatar