Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric interpretation for exact triangles consisting of projectively
  flat bundles on higher dimensional complex tori   Let $(X^n, \check{X}^n)$ be a mirror pair of an $n$-dimensional complex torus
$X^n$ and its mirror partner $\check{X}^n$. Then, a simple projectively flat
bundle $E(L,\mathcal{L})\rightarrow X^n$ is constructed from each affine
Lagrangian submanifold $L$ in $\check{X}^n$ with a unitary local system
$\mathcal{L} \rightarrow L$. In this paper, we first interpret these simple
projectively flat bundles $E(L,\mathcal{L})$ in the language of factors of
automorphy. Furthermore, we give a geometric interpretation for exact triangles
consisting of three simple projectively flat bundles $E(L,\mathcal{L})$ and
their shifts by focusing on the dimension of intersections of the corresponding
affine Lagrangian submanifolds $L$. Finally, as an application of this
geometric interpretation, we discuss whether such an exact triangle on $X^n$
($n \geq 2$) is obtained as the pullback of an exact triangle on $X^1$ by a
suitable holomorphic projection $X^n \rightarrow X^1$.

17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph