# algebraic map

A map $f:X\to Y$ between quasi-affine varieties $X\subset k^{n},Y\subset k^{m}$ over a field $k$ is called if there is a map $f^{\prime}:k^{n}\to k^{m}$ whose component functions are polynomials, such that $f^{\prime}$ restricts to $f$ on $X$.

Alternatively, $f$ is algebraic if the pullback map $f^{*}:C(Y)\to C(X)$ maps the coordinate ring of $Y$, $k[Y]$, to the coordinate ring of $X$, $k[X]$.

Title algebraic map AlgebraicMap 2013-03-22 13:53:41 2013-03-22 13:53:41 mathcam (2727) mathcam (2727) 7 mathcam (2727) Definition msc 14A10 algebraic