Introduction to Algebraic Geometry

Systems of algebraic equations......Page 5
Affine algebraic sets......Page 11
Morphisms of affine algebraic varieties......Page 17
Irreducible algebraic sets and rational functions......Page 25
Projective algebraic varieties......Page 35
Bézout theorem and a group law on a plane cubic curve......Page 49
Morphisms of projective algebraic varieties......Page 61
Quasi-projective algebraic sets......Page 73
The image of a projective algebraic set......Page 81
Finite regular maps......Page 87
Dimension......Page 97
Lines on hypersurfaces......Page 109
Tangent space......Page 121
Local parameters......Page 135
Projective embeddings......Page 151
Blowing up and resolution of singularities......Page 163
Riemann-Roch Theorem......Page 179
Index......Page 194