PlanetMath: algebraic map

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algebraic map

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

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

"algebraic map" is owned by mathcam. [ full author list (2) | owner history (1) ]

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Other names:

algebraic

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Cross-references: ring, coordinate, pullback, polynomials, functions, component, field, quasi-affine varieties, map
There are 62 references to this entry.

This is version 4 of algebraic map, born on 2003-08-22, modified 2006-08-10.
Object id is 4641, canonical name is AlgebraicMap.
Accessed 8493 times total.

Classification:

14A10 (Algebraic geometry :: Foundations :: Varieties and morphisms)

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