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Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
4
votes
Irreducible components of quotients of Cohen-Macaulay rings of the "correct" dimension
To complement Hailong's answer, here is another way of seeing that an irreducible component of a Cohen-Macaulay scheme need not have special properties. In the example below, the whole scheme is Cohen …
8
votes
When is a blow-up a non-trivial product?
I am interpreting the question as also implying that $X$ itself is not a product. I do not have an answer in general, but I think that I have an example. It is a projective surface with a singular p …