Let $X$ be a Cohen-Macaulay scheme (I will be interested in the case when this is ${\rm Spec}(A/I)$ where $A$ is a polynomial ring over a field and $I$ is a homogeneous ideal). I w …

When are (prime) ideals of a noetherian ring $R$ Cohen-Macaulay as $R-$modules? That is, $depth_R(Ann_R(P))=dim_R(R/Ann_R(P)$ for each $P\in {\rm Spec}(R)$

This is basically a question of functoriality for base change of CM morphisms. EDIT: $\text{ }$ Brian Conrad sent me an email explaining the that this is indeed true, and follow …

http://people.missouristate.edu/lesreid/reu/2007/PPT/robin.ppt it said missing part inside and not missing part outside is non Cohen-Macaulay semigroup which determine whether i …

Let $Z$ be an irreducible and reduced scheme. Does there exist a reduced complete intersection $Y$ such that $Z$ is an irreducible component of $Y$?

Show that for every m between 2 and n-2 there exists a prime ideal of height m in R=K[x1,x2,...xn] such that R/p is not Cohen-Macualay.

Given any reduced excellent scheme $X$, there exists a Macaulayfication $\pi : Y \to X$. In other words, there exists a proper birational map $\pi$ from a Cohen-Macaulay scheme $Y …

Suppose that $X$ is a Cohen-Macaulay normal scheme/variety and $\pi : Y \to X$ is a proper birational map with $Y$ normal. Question: Is $Y$ also Cohen-Macaulay? Are there commo …

In deformation theory, Cohen-Macaulay in codimension 2 is the first to be considered in higher order deformation. Does Cohen-Macaulay in codim. 2 have some good property to work wi …

Let $X$ be a (EDIT: non-singular, or even $\mathbf A^n$) algebraic variety over a field $k$ (alg. closed). Suppose $G$ is a finite group acting on $X$, $|G|\neq 0$ in $k$. Then $k[ …

Hi, my question is simple. Let (R,m) be a commutative regular local noetherian ring. Is it true that for every prime p \in Spec(R), the factor ring R/p has maximal cohen-macaulay …

I'm not sure how long this iterative questions can go on, but let me try again. Let's say $X$ is a Cohen-Macaulay scheme with an action of $\mathbb{G}_m$ (i.e. if $X$ is affine, a …

Suppose $R$ is a Cohen-Macaulay ring. It is well known that if $I$ is an ideal of $R$ generated by $n$ elements, and $I$ has codimension $n$, then $R/I$ is also Cohen-Macaulay. N …

$A$ a Cohen-Macaulay ring (not necessarily local), $M$ a Cohen-Macaulay $A$-module. Then does it necessarily follow that $\mbox{ann}(M)$ is height-unmixed?