Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fourier-Mukai transforms for coherent systems on elliptic curves   We determine all the Fourier-Mukai transforms for coherent systems consisting
of a vector bundle over an elliptic curve and a subspace of its global
sections, showing that these transforms are indexed by the positive integers.
We prove that the natural stability condition for coherent systems, which
depends on a parameter, is preserved by these transforms for small and large
values of the parameter. By means of the Fourier-Mukai transforms we prove that
certain moduli spaces of coherent systems corresponding to small and large
values of the parameter are isomorphic. Using these results we draw some
conclusions about the possible birational type of the moduli spaces. We prove
that for a given degree $d$ of the vector bundle and a given dimension of the
subspace of its global sections there are at most $d$ different possible
birational types for the moduli spaces.

12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat