Equidimensional scheme

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In algebraic geometry, a field of mathematics, an equidimensional scheme (or, pure dimensional scheme) is a scheme all of whose irreducible components are of the same dimension. All irreducible schemes are equidimensional. In affine space, the union of a line and a point not on the line is not equidimensional. In general, if two closed subschemes of some scheme, neither containing the other, have unequal dimensions, then their union is not equidimensional.

If a scheme is smooth or étale over Spec k for some field k, then every connected component (which may be larger than an irreducible component), is equidimensional.

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