 Codimension of an algebraic subvariety (source code)

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= Codimension of an algebraic subvariety
{title2=$\operatorname{codim}_X Y=\dim X-\dim Y$}

= Algebraic codimension
{synonym}

For an irreducible closed subvariety $Y$ of an irreducible variety $X$, its codimension is $\dim X-\dim Y$. In an affine chart it also equals the height of the corresponding <prime ideal>, by the dimension formula for finite-type domains over a field.

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