Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Boundness of intersection numbers for actions by two-dimensional
  biholomorphisms   We say that a group $G$ of local (maybe formal) biholomorphisms satisfies the
uniform intersection property if the intersection multiplicity $(\phi (V), W)$
takes only finitely many values as a function of $G$ for any choice of analytic
sets $V$ and $W$. In dimension $2$ we show that $G$ satisfies the uniform
intersection property if and only if it is finitely determined, i.e. there
exists a natural number $k$ such that different elements of $G$ have different
Taylor expansions of degree $k$ at the origin. We also prove that $G$ is
finitely determined if and only if the action of $G$ on the space of germs of
analytic curves have discrete orbits.

31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ