Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Poincare series of filtrations corresponding to ideals on surfaces   Earlier the authors considered and, in some cases, computed Poincare series
of two sorts of multi-index filtrations on the ring of germs of functions on a
complex (normal) surface singularity (in particular on the complex plane). A
filtration from the first class was defined by a curve (with several branches)
on the surface singularity. The other one (so called divisorial filtration) was
defined by a set of components of the exceptional divisor of a modification of
the surface singularity. Here we define a filtration corresponding to an ideal
or to a set of ideals in the ring of germs of functions on a surface
singularity and compute the corresponding Poincare series in some cases. For
the complex plane this notion unites the two classes of filtrations described
above.

7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an