By the end of this course, a student will:
- make use of the correspondence between algebraic varieties over an algebraically closed field k and finitely generated commutative k-algebras without nilpotents,
- determine basic properties of a given algebraic curve, compute its projective closure, degree, genus, singular and regular points,
- use Bezout’s theorem in order to prove various results including those about linear systems,
- understand and use the group law on an elliptic curve,
- resolve singularities using blow-ups,
- make computations and carry out proofs using the Riemann-Roch theorem.