Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The moduli stack of parabolic bundles over the projective line, quiver
  representations, and the Deligne-Simpson problem   In "Quantization of Hitchin's Integrable System and Hecke Eigensheaves",
Beilinson and Drinfeld introduced the "very good" property for a smooth complex
equidimensional stack. They prove that for a semisimple complex group G, the
moduli stack of G-bundles over a smooth complex projective curve X is "very
good", as long as X has genus g > 1. In the case of the projective line, when g
= 0, this is not the case. However, the result can sometimes be extended to the
projective line by introducing additional parabolic structure at a collection
of marked points and slightly modifying the definition of a "very good" stack.
We provide a sufficient condition for the moduli stack of parabolic vector
bundles over the complex projective line to be very good. We then use this
property to study the space of solutions to the Deligne-Simpson problem.

13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom