Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Hi,

I have a $m \times 2m$ matrix of linear forms over $\mathbb{C}[x,y,z,w]$. It is of the form $M = ( x I - A z -B w | y I - C z - D w$. Here $A,B,C$ and $D$ are $m \times m$ scalar matrices. Let $I$ be the ideal of maximal minors of $M$. I believe that the CM-regularity of this ideal is $m$. However I havve no idea how to show it.

This is not a generic determinantal ideal, so many results for them do not apply in this case. However maybe there is a way to specialize and still keep the CM-regularity.

In general I want to show that for matrices of different size the closed subschemes of $\mathbb{P}^3$ defined by the ideals are non-isomorphic. Under certain assumptions the subscheme will be one dimensional.

I'm not very familiar with results about the CM-regularity (outside Eisenbud's "Commutative Algebra"), so a reference of something will be appreciated as well.

Thanks.

share|improve this question

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.