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Erschienen in:
2017 | OriginalPaper | Buchkapitel
Algebraic Geometry
verfasst von : Nolan R. Wallach
Erschienen in: Geometric Invariant Theory
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This chapter is a compendium of results from algebraic geometry that we will use in the later chapters. The emphasis is on the relationship between the two natural topologies on an algebraic variety over the complex numbers, the Zariski topology and the metric topology (or standard topology) that comes from the embedding of certain open subsets in the Zariski topology (those that are isomorphic with affine varieties) as closed subsets in a finite-dimensional vector space. The interaction of these two topologies will be one of the main themes of the later chapters in this book. Many of the basic theorems in algebraic geometry (and differential geometry) are stated with references, many to [GW], while others are given proofs. There are complete proofs of most of the statements that relate to the interplay between algebraic and differential geometry.