Generally speaking, algebraic geometry deals with geometric objects defined by polynomial equations. We will cover topics 1-3 below, and maybe one other topic, depending on the level of the students.
- Topics from commutative algebra.
- Algebraic varieties over an algebraically closed field: definitions and main properties.
- Curves and their function fields.
- Intersection Theory in the projective plane.
- Vector bundles and coherent sheaves.
- Picard group and projective embeddings.
- Schemes: definitions, examples and basic properties.