The lecture will discuss the classical theory of algebraic curves. The topics will include: divisors, Riemann-Roch, linear systems, differentials, Clifford's theorem, curves on surfaces, singularities, curves in projective space, elliptic curves, hyperelliptic curves, families of curves, moduli, and enumerative geometry. There will be many examples and calculations.
For background, a semester course in algebraic geometry should be sufficient (perhaps even if taken concurrently). You should know the definitions of algebraic varieties and algebraic morphisms and their basic properties.
Exercise classes will take place roughly every two weeks on Thursdays, 14-15 (in the time slot and room of the lecture). Exercise sheets will be posted here a week in advance. You can hand in your solutions in the exercise class or in the corresponding box in HG J68. They will be corrected and returned during the next exercise class.
|Exercise sheet||Due by||Solutions|
|Exercise sheet 1||March 2||Solution sheet 1|
|Exercise sheet 2||March 16||Solution sheet 2|
|Self study: Sheaf cohomology||March 30||/|
|Exercise sheet 3||March 30||/|
|Exercise sheet 4||May 9||Solution sheet 4|
|Exercise sheet 5||June 1||Solution sheet 5|
The oral exam will last 20 minutes, in which you will be asked to answer questions and solve problems on the blackboard. The following sheet contains sample questions and you may be asked to explain the solution of some of them during the exam. The "Bonus" parts contain optional challenges and you are not required to be able to present a solution for those.