Q: On Cohen-Macaulay schemes I know that the irreducible components of a Cohen-Macaulay (CM) scheme don't need to be Cohen-Macaulay. But what happens if we assume that that the irreducible components are CM, what can we say about the scheme? More precisely my question is the following: 
Let $X$ be a reduced scheme of finite type over a field $K$ and suppose that the irreducible components of $X$ are Cohen-Macaulay. In which case is the scheme $X$ itself Cohen-Macaulay? 
