Contents Preface xi Introduction xiii Part 1. Algebraic Geometry Chapter 1. Affine and Projective Varieties 3 §1.1. Affine varieties 3 §1.2. Abstract affine varieties 17 §1.3. Projective varieties 19 Exercises 25 Chapter 2. Algebraic Varieties 27 §2.1. Prevarieties 27 §2.2. Varieties 31 Exercises 49 Part 2. Algebraic Groups Chapter 3. Basic Notions 55 §3.1. The notion of algebraic group 55 §3.2. Connected algebraic groups 56 §3.3. Subgroups and morphisms 59 §3.4. Linearization of affine algebraic groups 60 §3.5. Homogeneous spaces 65 §3.6. Characters and semi-invariants 66 vii
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