AG - Find the genus of the curve y^2=x(x-1)(x-2) by projecting it down to the y-axis.
AG - Let X be a variety. Take a divisor D over X. What it does mean that D is ample ?
AG - Take an elliptic curve. Give an example of a divisor which is ample but not very ample. 
Prove your assertion. For that divisor, what are the global sections for the corresponding invertible sheaf.
LO - How many countable models of arithmetic are there ?
LO - How does a non standard model of arithmetic look like ?
LO - The theory of a model is categorical iff the model is .... (fill in the gap).
LO - Give an example of \Aleph_o categorical theory but not uncountable categorical.