What is the flaw in the answer for proving any rational function on PP^1 is constant? Le

Taylor Haines 2022-02-15 Answered
What is the flaw in the answer for proving any rational function on PP1 is constant?
Let ϕ:PP11 be a rational function. Since 1PP1 we can think ϕ:PP1PP1 as rational function. As every rational map from PP1PPn is regular, so ϕ is regular. We also know that any regular function on PP1 is constant, so ϕ is constant.
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Zernerqcw
Answered 2022-02-16 Author has 11 answers
A regular function on a variety X is, by definition, a regular map X1. Just because every regular function on PP1 is constant, that doesn't mean that every regular map to a variety other than 1 is constant. In particular, ϕ, being a regular map PP1PP1, need not be constant.
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