Contents

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Introduction 2

0. Algorithms for Polynomials 4

1. Algebraic Sets 14

2. Affine Algebraic Varieties 30

3. Algebraic Varieties 44

4. Local Study:T angent Planes, Tangent Cones, Singularities 59

5. Projective Varieties and Complete Varieties 80

6. Finite Maps 101

7. Dimension Theory 109

8. Regular Maps and Their Fibres. 117

9. Algebraic Geometry over an Arbitrary Field 131

10. Divisors and Intersection Theory 137

11. Coherent Sheaves; Invertible Sheaves. 143

12. Differentials 149

13. Algebraic Varieties over the Complex Numbers 151

14. Further Reading 153

Index 156

_c 1996, 1998 J.S. Milne. You may make one copy of these notes for your own personal use.

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2 J.S. MILNE

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