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Math Help - Algebraic Geometry - D&F Section 15.1, Exercose 24

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    Algebraic Geometry - D&F Section 15.1, Exercose 24

    Dummit and Foote Section 15.1, Exercise 24 reads as follows:

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    Let  V = \mathcal{Z} (xy - z) \subseteq \mathbb{A}^3 .

    Prove that V is isomorphic to  \mathbb{A}^2

    and provide an explicit isomorphism  \phi  and associated k-algebra isomorphism  \widetilde{\phi} from  k[V] to  k[ \mathbb{A}^2] along with their inverses.

    Is  V = \mathcal{Z} (xy - z^2)  isomorphic to  \mathbb{A}^2 ?

    -------------------------------------------------------------------------------------------------------------

    I would appreciate some help and guidance with getting started with this exercise [I suspect I might need considerable guidance! :-( ]


    Some of the background and definitions are given in the attachment.


    Peter
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