Noncommutative Analysis

Tag: essential normality

Stable division and essential normality: the non-homogeneous and quasi homogeneous cases

Update (January 29, 2016): paper revised, see this post

 

Several months ago Shibananda Biswas (henceforth: Shibu) and I posted to the arxiv our paper “Stable division and essential normality: the non-homogeneous and quasi homogeneous cases“. I was a little too busy to write about it at the time, but now that it is summer it seems like a good time to do it, since I am too busy, and I need a break from work. Nothing like going back and thinking about papers you have already written when you are overwhelmed by your current project.

Anyway, the main problem the paper I wrote with Shibu deals with, is the essential normality of submodules of various Hilbert modules (closely related to the Drury-Arveson module that I wrote about in the past: one, two, three, or if you are really asking for trouble, look at this survey). This paper is highly technical, and I want to try to explain it in a non-technical fashion. Read the rest of this entry »

Essential normality and the decomposability of algebraic varieties

I am very proud, because few days ago Matt Kennedy and I have had our new paper, Essential normality and the decomposability of algebraic varieties, published in the New York Journal of Mathematics.

In this paper we treat a strong version of a conjecture of Arveson, which we call the “Geometric Arveson-Douglas Conjecture”, and we obtain some new results in particular cases (the conjecture is still far from being settled). I think that we do a good job in the introduction of the paper explaining what this conjecture is and what we do, so I invite you to take a look.

Now I want to say a few words about the New York Journal of Mathematics. I’ll say it in a different post.