Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regular multi-types and the Bloom conjecture   We prove equality of the vector field (iterated commutator) type and the
regular contact type, which together with the Bloom theorem on equality of the
Levi-form type and the regular contact type provides a complete solution of a
long standing open problem of Bloom in the case of complex dimension three. For
general dimensions, we verify the Bloom conjecture when $s=n-2$, which provides
the first positive result in the pseudoconvexity sensitive case for a real
hypersurface in ${\mathbb{C}}^n$ after his important work in 1981.

27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom