Homework for Week 5

Part 1

Prove that if X consists of two points, then k[X] ≅ k ⊕ k. (Note: we will define ⊕ in class on Tuesday.)

Part 2

1. Blow up the curve y²=x³ at the origin. Compare the blow-up to the original curve (e.g.: how do they differ? what is the dimension of each?).
2. Calculate dim (X x Y) in terms of dim X and dim Y.

• Part 1: Due Tuesday
• Part 2: Due Thursday