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Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.

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Irreducible component of a Cohen-Macaulay variety

Is it true that an irreducible component of a Cohen-Macaulay variety is also Cohen-Macaulay? If not, then in what cases does this fact hold?
Nham Ngo's user avatar