1
$\begingroup$

Could anyone give me a hint how to show this one:

Let $V$ be a finite set of points in projective space. How to show that the coordinate ring of $V$ is Cohen-Macaulay?

  • 0
    Just to check, when you say coordinate ring, you mean that you have $X \subset \mathbb{P}^n$ and you are looking at the corresponding homogenous quotient of $\mathbb{C}[x_0, \ldots, x_n]$, right? @Georges Elencwajg's hint assumes that you mean $H^0(X, \mathcal{O})$, which is also a reasonable interpretation, but makes this question very easy, so I don't think it's what you mean.2012-05-14

1 Answers 1

2

Proof 1: Regular $\implies$ Cohen-Macaulay.

Proof 2: Artinian $\implies$ Cohen-Macaulay.