Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stable division and essential normality: the non-homogeneous and quasi
  homogeneous cases   Let $\mathcal{H}_d^{(t)}$ ($t \geq -d$, $t>-3$) be the reproducing kernel
Hilbert space on the unit ball $\mathbb{B}_d$ with kernel \[ k(z,w) =
\frac{1}{(1-\langle z, w \rangle)^{d+t+1}} . \] We prove that if an ideal $I
\triangleleft \mathbb{C}[z_1, \ldots, z_d]$ (not necessarily homogeneous) has
what we call the "approximate stable division property", then the closure of
$I$ in $\mathcal{H}_d^{(t)}$ is $p$-essentially normal for all $p>d$. We then
show that all quasi homogeneous ideals in two variables have the stable
division property, and combine these two results to obtain a new proof of the
fact that the closure of any quasi homogeneous ideal in $\mathbb{C}[x,y]$ is
$p$-essentially normal for $p>2$.

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The categories of this paper are: hep-ph
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol