Timeline for What is the meaning of "algebraic construction", and how could this be used in algebraic geometry
Current License: CC BY-SA 3.0
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| Jul 20, 2013 at 0:05 | comment | added | user36938 | @Jeremey: Sure, all I meant is that what looks like a "square root" from one point of view may be a "coordinate" from another; for the plane curve $C$ defined by $y^2 = f(x)$ one could say that the map $y:C \rightarrow \mathbf{A}^1$ is $P \mapsto \sqrt{f(x(P))}$. | |
| Jul 19, 2013 at 19:25 | comment | added | Jérémy Blanc | No, square roots are not allowed for a rational map. If you want a rational map from a variety $X$ to a variety $Y$, the image of a point $x\in X$ should depend algebraically from the coordinates in $X$ (i.e. be quotient of polynomials). | |
| Jul 19, 2013 at 3:40 | comment | added | user36938 | As you know, square roots would be OK - we would just call it ``$y$'' and write $y^2 = f(x)$, etc. Exp and log would be another matter. :) | |
| Jul 18, 2013 at 19:02 | history | answered | Jérémy Blanc | CC BY-SA 3.0 |