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So I have two varieties;
$V=V(y-x^2)$ and $W=V(y^2-x^3)$

$\phi: V \mapsto W$; $(x,y) \mapsto (y,xy)$
define
$\phi^*: C[W] \mapsto C[V]$; $[f] \mapsto [f o \phi]$

This is the morphism i'm looking at;
$\gamma: V \mapsto W$ by $(x,y) \mapsto (x^2,xy)$

Can anyone tell me what $\gamma(x,y)$ is? Also, how do you compute $\gamma^*:C[W] \mapsto C[V] $? Apparently it is the same as $\phi^*$

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    Geometrically, this says that the functions $y$ and $x^2$ are different functions on the entire affine plane, but they restrict to the same function on the parabola $V$ given by the equation $y = x^2$.2012-05-16

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