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One of the most fundamental questions one can ask about an algebraic curve is how it may be mapped to projective space. For instance, every elliptic curve has a Weierstrass equation representing it as the zero set of a cubic polynomial in the plane, and this is very useful for studying it. There are many interesting questions involved in generalizing this to other types of curves, and other projective spaces. Surprisingly, there are interesting open questions even for maps from the projective line to itself.