Abstract

AbstractIn this chapter, we collect all the necessary background to follow the further discussion on geometric invariant theory and moduli spaces. First we recover the notions of algebraic (affine and projective) variety and actions of algebraic groups, which will be the features in GIT quotients. Then we include a brief summary of sheaves, cohomology, and schemes, because those are the objects with which to develop this theory in full generality. Finally, essentials about holomorphic vector bundles, line bundles, and divisors are discussed.

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