Alg. Geom. Regular function confusion

[Bleys]

So in class today the lecturer gave a regular map on the set $V(s_{1}s_{2}-s_{0}^2)$ in projective 2-space to projective 1-space by $\phi = (s_{0}:s_{1})=(s_{2}:s_{0})$.
I'm confused. Is that another representation of the "function"? (Meaning they map to the same point classes?) or is it an alternate description on where the other is non defined?
I mean, it can't be the first option, since if the s_{0}=0 then the other two must be zero, but there is no such point in projective space.
But, I just want to make sure it really is the other option and not be something else I missed.

 

[mathwonk]

this makes no sense. your input point is not a point of P^2.

 

[Bleys]

?? $\phi$ takes a point $(s_{0}:s_{1}:s_{2})$ to $(s_{0}:s_{1})$ and/or $(s_{2}:s_{0})$