Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Counting curves on a general linear system with up to two singular
  points   In this paper we obtain an explicit formula for the number of curves in a
compact complex surface $X$ (passing through the right number of generic
points), that has up to one node and one singularity of codimension $k$,
provided the total codimension is at most $7$. We use a classical fact from
differential topology: the number of zeros of a generic smooth section of a
vector bundle $V$ over $M$, counted with signs, is the Euler class of $V$
evaluated on the fundamental class of $M$.

34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org