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Beginning Concepts

In: Introduction to Algebraic Geometry

Author

Listed:
  • Igor Kriz

    (University of Michigan, Department of Mathematics)

  • Sophie Kriz

    (University of Michigan, Department of Mathematics)

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.

Suggested Citation

  • Igor Kriz & Sophie Kriz, 2021. "Beginning Concepts," Springer Books, in: Introduction to Algebraic Geometry, chapter 1, pages 1-55, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-62644-0_1
    DOI: 10.1007/978-3-030-62644-0_1
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