Viewed 8k times. The algebraic interpretation is usually the one we see and the question is whether it can be put in geometric terms, that is, terms that we traditionally associate with geometry. Home Questions Tags Users Unanswered. One meaning of the Cohen—Macaulay condition can be seen in coherent duality theory. Multiplicity one criterionon the other hand, roughly characterizes a regular local ring as a local ring of multiplicity one. You can see this geometrically by the way it is non-normal if it is at all. Ordered Sets pp Cite as. By using this site, you agree to the Terms of Use and Privacy Policy.

In mathematics, a Cohen–Macaulay ring is a commutative ring with some of the 1 Definition; 2 Examples; 3 Geometric consequences; 4 Miracle flatness or. In this hour we will talk about, or build up to talking about, Cohen-Macaulay rings.

Definition: Let (A, m,k) be a Noetherian local ring and M a finite A-module.

So, I would say that the geometric meaning of Cohen-Macaulay is that it is a space of a curve in the moduli stack of the corresponding moduli problem). in the Cohen-Macaulay definition of depth, a homological condition.

This theory has given birth to the concept of lexicographically shellable posets.

Question feed. These properties are of course best for seeing which schemes are not CM, e.

## An Introduction to CohenMacaulay Partially Ordered Sets SpringerLink

The geometric meaning of Corollary Some of them are already mentioned in this question nice intersection property, good duality, combinatorial meaning etc. The algebraic interpretation is usually the one we see and the question is whether it can be put in geometric terms, that is, terms that we traditionally associate with geometry. Skip to main content.

JAMES Cohen-Macaulay modules over Cohen~Macaulay rings.

Rota On the foundations of combinatorial theory: I.

Video: Cohen macaulay modulus of elasticity Elasticity & Hooke's Law - Intro to Young's Modulus, Stress & Strain, Elastic & Proportional Limit

Then X is Cohen—Macaulay if and only all fibers of f have the same degree. Now assume that you are given a surface, given by some homogeneous equations, how do you "see" if it is CM or not?

I usually think of Krull dimension as going from small to large: We start with a closed point, embed it into a curve, then to a surface until we get to the maximal dimension. The ring R is called Cohen—Macaulay if its depth is equal to its dimension.

Video: Cohen macaulay modulus of elasticity Elasticity - Modulus

Any time you can connect a homological to a geometric property, one has some interesting and non-trivial result.

Cohen macaulay modulus of elasticity |
Eisenbud and C.
Baclawski Whitney numbers of geometric lattices, Advances In Math 16, — Combinatorial properties of some important posets will be surveyed. But the answers here reveal some more insights, thanks! Karl Schwede Karl Schwede |

Baclawski Whitney numbers of geometric lattices, Advances In Math 16, — Then X is Cohen—Macaulay if and only all fibers of f have the same degree.

Hailong's answer contains the link to How to think about CM rings?

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