Re: Surjective Morphism

jones.tessa@xxxxxxxxx wrote:
Let V=Z(xz-y^2, yz-x^3, z^2-x^2y) in A^3.
Prove that map b:A^1 -> V defined by b(t)=(t^3, t^4, t^5) is a
surjective morphism.

I stared by assuming that if (x,y,z) != (0,0,0) then t=x/y.
What happens next?

Wrong way, you probably meant t := y/x.

Actually, the wording of the original problem is a bit misleading,
what you want is that the image of the morphism

b: A^1 --> A^3 defined by b(t)=(t^3, t^4, t^5)

coincides with V. Obviously it is contained in V.

First you should check, that for each point (0,0,0) =/= (x,y,y) in V,
you have xyz =/=0 i.e., every coordinate is nonzero.

Then show y/x = z/y and (y/x)^3 = x .

Marc
.

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