Algebraic Geometry:
1) Let X be a quintic in P^2.  Calculate H^0 and H^1 of the normal bundle (I
used the ses of sheaves given by restriction)
1a) Do the calculation again using a different method (Riemann Roch)
2) Calculate H^0 and H^1 of the normal bundle for a curve cut out by a
complete intersection in P^3 of two surfaces of degrees n and m respectively.
3) Since I wasn't able to do (2) immediately we digressed into a sequence of
questions:  What is degree of a vector bundle?  How is it defined?  What is
Riemann Roch for vector bundles? What is the first chern class of a vector
bundle that is the direct sum of line bundles? What happens when you take
Tensor/Exterior powers?  What if your bundle is not the direct sum of line
bundles?
5) What is the dimension of all genus 6 curves (genus(X) = 6)?
4) What is the meaning of the normal bundle?  (as related to the moduli space
above)
3) Is your quintic hyperelliptic?
4) What is the dimension of hyperelliptic genus 6 curves?  What is the
dimension of genus 6 curves in P^2?  Do these spaces intersect in the moduli
space of all genus 6 curves?
5) Over a smooth base can a genus 6 curve be deformed into a line?  Why?  What
are some invariants of smooth families?
6) What can cause the moduli space of __ to change in dimension?  What happens
at singularities/ what can cause a singularity
7) Define the hilbert polynomial?