Beginning Concepts

Igor Kriz () and Sophie Kriz ()
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Igor Kriz: University of Michigan, Department of Mathematics
Sophie Kriz: University of Michigan, Department of Mathematics

Chapter 1 in Introduction to Algebraic Geometry, 2021, pp 1-55 from Springer

Abstract: Abstract The purpose of this chapter is to give a quick introduction to algebraic varieties, which will give us an idea of what algebraic geometry studies. In contrast with, say, differential geometry, almost no prerequisites are needed to start with. In particular, no analysis is required: All the foundations come from algebra. We begin this chapter by assuming the key results from algebra as given, and define the first concepts of algebraic geometry in Sect. 1. After that, some concepts from category theory and universal algebra will become necessary, which are introduced in Sect. 2. In Sect. 3, some additional geometrical concepts are introduced.

Date: 2021
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DOI: 10.1007/978-3-030-62644-0_1

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