Course Content (Syllabus)
Affine Varieties: Algebraic Sets in Αn, Affine and quasi-affine Varieties, Hilbert's Nullstellensatz, Coordinate Rings, Noether's Spaces. Projective Varieties: Algebraic Sets in Pn, Projective Nullstellensatz, Projective Closure of an Affine Variety. Morphisms of Varieties: Regular Functions, Function Fields of One Variable, Basic properties of Morphisms, Finite Morphisms, Rational maps. Product of Varieties: Product of Affine Varieties, Product of Projective Varieties, Segree's Embedding, Image of a Projective variety. Dimension: Dimension of a Topological Space, Krull's Dimension, Dimension of the Intersection of a Variety with a hypersurface, Dimension and Morphisms. Local Properties.