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1answer
124 views

Does projective duality preserve arithmetic-Cohen-Macaulay-ness?

Let $V$ be a vector space over $\mathbb{C}$. Suppose $X\subset \mathbb{P} V$ is an algebraic variety, and consider its projective dual variety $X^\vee \subset \mathbb{P} V^*$. If the coordinate ring ...
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0answers
148 views

A doubt from the paper “The diagonal subring and the Cohen-Macaulay property of a multigraded ring”

I am currently reading the paper "The diagonal subring and the Cohen-Macaulay property of a multigraded ring" by Eero Hyry. I have a doubt about the first part of Theorem 2.5. In the proof $(1)\iff ...
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0answers
25 views

Maximal Cohen-Macaulay modules of type one

Does any body know an example of a Noetherian local ring (R,m) which admits a maximal cohen-macaulay module of type one, but the ring R itself is not CM. If C is the maximal CM module then the type ...
5
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1answer
232 views

Can one prove that toric varieties are Cohen-Macaulay by finding a regular sequence?

It's well-known that if $P$ is a finitely generated saturated submonoid of $\mathbb{Z}^n$, then the monoid algebra $k[P]$ is Cohen-Macaulay (at the maximal ideal $m = (P-0)k[P]$). However, all proofs ...
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0answers
86 views

Producing local complete intersection curves in singular surfaces

Let $X$ be a smooth surface in $\mathbb{P}^3$ and $C$ a local complete intersection curve in $X$. Does there exist a hyperplane $H$ in $\mathbb{P}^3$ such that $C$ is a local complete intersection ...
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1answer
392 views

When is the reduced subscheme of a Cohen-Macaulay scheme also Cohen-Macaulay?

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 would like to know ...
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0answers
117 views

ideals of a noetherian ring $R$ Cohen-Macaulay as $R-$modules

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 $P\in {\rm Spec}(R)$
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1answer
84 views

What is the way to after finding Cohen-Macaulay semigroup as ring of monomial?

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 is missing in the ...
5
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1answer
335 views

Base change of trace for Gorenstein or Cohen-Macaulay morphisms

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 follows from his book. ...
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1answer
317 views

Irreducible components of reduced complete intersection

Let $Z$ be an irreducible and reduced scheme. Does there exist a reduced complete intersection $Y$ such that $Z$ is an irreducible component of $Y$?
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0answers
267 views

Simple proof of that $k[X]^G$ Cohen-Macaualy ($G$ finite)?

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 $k[X]^G$ is ...
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1answer
486 views

Why are people interested in Cohen-Macaulay of codimension 2?

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 with? Does it somehow ...
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1answer
368 views

Normal Macaulayfications

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 $Y$ to $X$. These ...
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1answer
180 views

CM module is height-unmixed?

$A$ 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?
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3answers
458 views

Maximal Cohen Macaulay modules over regular factor rings.

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 R/p-module? Best ...
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2answers
408 views

Are schematic fixed-points of a Cohen-Macaulay scheme 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 grading on the ...
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2answers
798 views

Blowups of Cohen-Macaulay varieties

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 common conditions which ...
3
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2answers
368 views

Irreducible components of quotients of Cohen-Macaulay rings of the “correct” dimension

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. Now suppose that $I$ ...