For questions on birational geometry, a field of algebraic geometry the goal of which is to determine when two algebraic varieties are isomorphic outside lower-dimensional subsets.
Questions tagged [birational-geometry]
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Degree $2$ birational map of $\mathbb{P}^1$
I know that there are many examples of birational degree $2$ projective maps.
One example based on the $2$-dimensional Lyness map is
$$ \varphi([x,y,z]) = [x y, yz + z^2, x z] $$
with inverse map
$$ \psi([x,y,z]) = [x z+z^2, x y, y z]. $$
The…
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