Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A vector bundle version of the Monge-Ampere equation   We introduce a vector bundle version of the complex Monge-Ampere equation
motivated by a desire to study stability conditions involving higher Chern
forms. We then restrict ourselves to complex surfaces, provide a moment map
interpretation of it, and define a positivity condition (MA positivity) which
is necessary for the infinite-dimensional symplectic form to be Kahler. On
rank-2 bundles on compact complex surfaces, we prove two consequences of the
existence of a "positively curved" solution to this equation - Stability
(involving the second Chern character) and a
Kobayashi-Lubke-Bogomolov-Miyaoka-Yau type inequality. Finally, we prove a
Kobayashi-Hitchin correspondence for a dimensional reduction of the
aforementioned equation.

20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph