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Ben McKay
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The uniform position theorem says that the points of a general hyperplane section of an irreducible curve lie in uniform position. Doesn't that impyimply that the points of a general subspace of codimension k$k$ of an irreducible variety of dimension k$k$ lie in uniform position?

The uniform position theorem says that the points of a general hyperplane section of an irreducible curve lie in uniform position. Doesn't that impy that the points of a general subspace of codimension k of an irreducible variety of dimension k lie in uniform position?

The uniform position theorem says that the points of a general hyperplane section of an irreducible curve lie in uniform position. Doesn't that imply that the points of a general subspace of codimension $k$ of an irreducible variety of dimension $k$ lie in uniform position?

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user46071
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Uniform position principle

The uniform position theorem says that the points of a general hyperplane section of an irreducible curve lie in uniform position. Doesn't that impy that the points of a general subspace of codimension k of an irreducible variety of dimension k lie in uniform position?