Codimension

In mathematics, codimension is a basic geometric idea that applies to subspaces in vector spaces, to submanifolds in manifolds, and suitable subsets of algebraic varieties.

For affine and projective algebraic varieties, the codimension equals the height of the defining ideal. For this reason, the height of an ideal is often called its codimension.

The dual concept is relative dimension.

1 Definition

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2 Additivity of codimension and dimension counting

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3 Dual interpretation

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4 In geometric topology

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5 See also

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6 References