Lecture Notes for Algebraic geometry

Overview & Synopsis

This note covers notation, What is algebraic geometry, Affine algebraic varieties, Projective algebraic varieties, Sheaves, ringed spaces and affine algebraic varieties, Algebraic varieties, Projective algebraic varieties, revisited, Morphisms, Products, Dimension, The fibres of a morphism, Sheaves of modules, Hilbert polynomials and Bezouts theorem, Products of preschemes, Proj and projective schemes, More properties of schemes, More properties of schemes, Relative differentials, Locally free sheaves and vector bundles, Cartier divisors, Rational equivalence and the chow group, Proper push forward and flat pull back, Chern classes of line bundles.