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.
- Dundas, Bjorn Ian; Jahren, Björn; Levine, Marc; Østvær, P.A.; Röndigs, Oliver; Voevodsky, Vladimir (2007), Motivic Homotopy Theory: Lectures at a Summer School in Nordfjordeid, Norway, August 2002, Springer, p. 101, ISBN 9783540458975.
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