Exercises in bold are suggestions for topics for the obligatory assignment presentations on Thursdays. The other exercises are for training purposes. If you have another topic suggestion for the obligatory assignment presentation, please get in touch!
Chapter 1
- Affine normal rational curves. Exercise 1.11 (suggestion: show a picture for d=2 and d=3)
- Cones and homogeneous polynomials. Exercise 1.8 and 1.9.
Some training exercises: 1.1, 1.2, 1.5, 1.6, 1.7
Chapter 2
- Show that the space of nxn matrices with zero determinant is an irreducible algebraic variety (I.e. present Example 2.4 and a solution to Exercise 2.1). Discuss the set W_r of matrices of rank r.
Some training exercises: 2.4, 2.6, 2.9, 2.10, 2.11