Basic Notions

Igor R. Shafarevich
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Igor R. Shafarevich: Steklov Mathematical Institute of the Russian Academy of Sciences, Algebra Section

Chapter Chapter 1 in Basic Algebraic Geometry 1, 2013, pp 3-81 from Springer

Abstract: Abstract The chapter defines affine and quasiprojective varieties and two classes of functions on them, regular and rational. The former give the affine coordinate ring and the latter the field of rational functions. The notions of products of varieties and their dimension are discussed. In addition to definitions and their basic corollaries, proofs of several nontrivial results are given, including properness and dimensions of intersections.

Keywords: Quasiprojective Variety; Irreducible Plane Algebraic Curve; Affine Variety; Birational Equivalence; Isomorphic Inclusion (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-37956-7_1

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DOI: 10.1007/978-3-642-37956-7_1

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