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The Topology of Algebraic Varieties

In: Basic Algebraic Geometry 2

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  • Igor R. Shafarevich

    (Steklov Mathematical Institute)

Abstract

We saw in Chap. II, 2.3 that the set of complex points of an algebraic variety X defined over the field C of complex numbers is a topological space. In Chap. II, 2.3, this was proved for quasiprojective varieties, at the time the only varieties known to us. But the same arguments are valid also for arbitrary varieties. We give here a general definition; the topology of X that comes from its structure of a scheme is called its Zariski topology.

Suggested Citation

  • Igor R. Shafarevich, 1994. "The Topology of Algebraic Varieties," Springer Books, in: Basic Algebraic Geometry 2, edition 0, chapter 0, pages 117-151, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-57956-1_3
    DOI: 10.1007/978-3-642-57956-1_3
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