Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Moduli Spaces of semistable rank 2 co-Higgs bundles over $\mathbb{P}^1
  \times \mathbb{P}^1$   It has been observed, by S. Rayan, that the complex projective surfaces that
potentially admit non-trivial examples of semistable co-Higgs bundles must be
found at the lower end of the Enriques-Kodaira classification. Motivated by
this remark, it is natural to study the geometry of these objects over
$\mathbb{P}^1 \times \mathbb{P}^1$. In this paper, we present necessary and
sufficient conditions on the Chern classes $c_1,c_2$ of a bundle that guarantee
the non-emptiness of the moduli space $\mathcal{M^{\text{co}}}(c_1,c_2)$ of
rank 2 semistable co-Higgs bundles over $\mathbb{P}^1 \times \mathbb{P}^1$ (we
do this with respect to the standard polarization). We also give an explicit
description of the moduli spaces for certain choices of $c_1$ and $c_2$.

20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat