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I can't figure out this exercise: i have this singular curve in $\mathbb{P}^2\mathbb{C}$ given by $\{[X,Y,Z]\in \mathbb{P}^2\mathbb{C}:X^2Y^2+Y^2Z^2+X^2Z^2=0\}$, I have shown that its desingularization is a curve of genus zero, but now I must find an explicit isomorphism with the Riemann sphere. I don't know how to do it, could anybody help me with that? thank you

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    no, i can't see the isomorphism between the curve and $X^2 + Y^2 + Z^2=0$ because i thought $ X \mapsto XY, Y \mapsto YZ, Z \mapsto XZ$ but it doesen't seem to be working...2012-01-28

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