Compulsory assignment (before or on March 2nd.)

Possibly in pairs, present during a lecture 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 determinantal 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 ThenSegre product is a projective variety

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

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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

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