Compulsory assignment (due before March 1st.)

Possibly in pairs, present in up to 20 min one of the following (the list may be extended):

1.  Exercise 1.11  (affine normal rational curve X), and show that X is determinental algebraic set.

2. Exercise 2.11 + generalization from 3 variables, to n variables.

3. Prop 2.62 (the set of (m x n)- matrices of rank at most r is  irreducible)

4. Prop 2.64 (the set of quadratic forms in n variables of rank at most r is irreducible) 

5. Prop 5.16. (d+3 general points in d-space lies on a unique rational normal curve of degree d)

6. Prop 5.20 Segre product is a projective variety

7. The 5.31.  Hilbert Nullstellensatz in the product of projective space. 

At most one pair for each topic, on a first come first serve order.  Send an email to me when you have decided, and I will approve what is not taken and we find a date for the presentation.

Kristian R