 
Summary: Problem Set 4
Let V be a closed ane variety in An
k and let W be a closed ane variety in
Am
k . The product of V and W will be dened as
V × W = {(a1, . . . , an, b1, . . . , bm)(a1, . . . , an) V and (b1, . . . , bm) W}.
Problem 1. Let V be a closed ane variety in An
k and let W be a closed ane
variety in Am
k . Show that V × W is a close ane variety in An+m
k .
Problem 2. Consider the closed ane variety V (Y 2
 X) A2
C. Show that
V (Y 2
 X) is irreducible. (Hint: Show that I(V (Y 2
 X)) is prime).
Problem 3. Let I = (Y 4
 X2
, Y 4
