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Alg. Geom. Regular function confusion

  1. Oct 20, 2011 #1
    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].
    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.
  2. jcsd
  3. Oct 23, 2011 #2


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    this makes no sense. your input point is not a point of P^2.
  4. Oct 24, 2011 #3
    ?? [itex]\phi[/itex] takes a point [itex](s_{0}:s_{1}:s_{2})[/itex] to [itex](s_{0}:s_{1})[/itex] and/or [itex](s_{2}:s_{0})[/itex]
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