Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A codimension two CR singular submanifold that is formally equivalent to
  a symmetric quadric   Let $M\subset \mathbb{C}^{n+1}$ ($n\geq 2$) be a real analytic submanifold
defined by an equation of the form: $w=|z|^2+O(|z|^3)$, where we use $(z,w)\in
\mathbb{C}^{n}\times \mathbb{C}$ for the coordinates of $\mathbb{C}^{n+1}$. We
first derive a pseudo-normal form for $M$ near 0. We then use it to prove that
$(M,0)$ is holomorphically equivalent to the quadric $(M_\infty: w=|z|^2,0)$ if
and only if it can be formally transformed to $(M_\infty,0)$. We also use it to
give a necessary and sufficient condition when $(M,0)$ can be formally
flattened. The result is due to Moser for the case of $n=1$.

21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph