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- W77329767 abstract "In Chapter 1 the theory of algebraic varieties was developed along the lines of the theory of differentiable manifolds. In the present chapter, we shall analyse some notions and properties that are specific to algebraic varieties and either have no differentiable analogue or require an essentially different approach. The former comprise the notions of irreducibility and normality, rational maps, and blowings-up. The latter, those of completeness, dimension, and smoothness. This is also where the fundamental properties of algebraic varieties are established, namely, the theorem on the dimension of fibres, the theorem on the constructibility of the image, the connectedness theorem, the Zariski Main Theorem, the completeness of projective varieties, the finiteness theorem, etc. For this we shall have recourse to somewhat more algebra than we did in Chapter 1." @default.
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- W77329767 date "1994-01-01" @default.
- W77329767 modified "2023-09-26" @default.
- W77329767 title "Algebraic Varieties: Fundamental Properties" @default.
- W77329767 doi "https://doi.org/10.1007/978-3-642-57878-6_7" @default.
- W77329767 hasPublicationYear "1994" @default.
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