So in class today the lecturer gave a regular map on the set [itex]V(s_{1}s_{2}-s_{0}^2)[/itex] in projective 2-space to projective 1-space by [itex]\phi = (s_{0}:s_{1})=(s_{2}:s_{0})[/itex].(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Alg. Geom. Regular function confusion

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