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Problem Set 4 Let V be a closed ane variety in An
 

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

  

Source: Abo, Hirotachi - Department of Mathematics, University of Idaho

 

Collections: Mathematics