Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Counting stable sheaves on singular curves and surfaces   Given a quasi-projective scheme M over complex numbers equipped with a
perfect obstruction theory and a morphism to a nonsingular quasi-projective
variety B, we show it is possible to find an affine bundle M'/ M that admits a
perfect obstruction theory relative to B. We study the resulting virtual cycles
on the fibers of M'/B and relate them to the image of the virtual cycle [M]^vir
under refined Gysin homomorphisms. Our main application is when M is a moduli
space of stable codimension 1 sheaves with a fixed determinant L on a
nonsingular projective surface or Fano threefold, B is the linear system |L|,
and the morphism to B is given by taking the divisor associated to a coherent
sheaf.

3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex