Géométrie algébrique

MATH 4209: Introduction to algebraic geometry

1) Basic concepts: Zariski Topology on affine  and projective spaces. Plane affine curves: conics, rational curves, simple points

2) Closed algebraic subsets of affine spaces over an algebraically closed field, Affine algebra, Irreducible decomposition. Nullstellensatz. Morphisms.

3) Closed algebraic subsets of projective spaces.

4) Rational and regular functions. Rational functions. Sheaf of regular functions. Quasi projective varieties as ringed spaces.

5) Dimension theory.

6) Algebraic curves. Local rings of smooth algebraic curves. Divisors. Riemann-Roch theorem.