The Topology of Algebraic Varieties

Igor R. Shafarevich
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Igor R. Shafarevich: Steklov Mathematical Institute

Chapter Chapter VII in Basic Algebraic Geometry 2, 1994, pp 117-151 from Springer

Abstract: 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.

Keywords: Topological Space; Algebraic Variety; Euler Characteristic; Algebraic Curf; Differentiable Manifold (search for similar items in EconPapers)
Date: 1994
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DOI: 10.1007/978-3-642-57956-1_3

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