Dimension of an algebraic variety

In mathematics, the dimension of an algebraic variety V in algebraic geometry is defined, informally speaking, as the number of independent rational functions that exist on V.

Related Topics:
Mathematics - Algebraic variety - Algebraic geometry - Rational function

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For example, an algebraic curve has by definition dimension 1. That means that any two rational functions F and G on it must satisfy some polynomial relation

Related Topics:
Algebraic curve - Polynomial

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:P(F,G) = 0.

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That implies that F and G are constrained to take related values (up to some finite freedom of choice): they cannot be truly independent.

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