Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rank loci in representation spaces of quivers   Rank functors on a quiver $Q$ are certain additive functors from the category
of representations of $Q$ to the category of finite-dimensional vector spaces.
Composing with the dimension function on vector spaces gives a rank function on
$Q$. These induce functions on $\rep(Q, \alpha)$, the variety of
representations of $Q$ of dimension vector $\alpha$, and thus can be used to
define "rank loci" in $\rep(Q, \alpha)$ as collections of points satisfying
finite lists of linear inequalities of rank functions. Although quiver rank
functions are not generally semicontinuous like the rank of a linear map, we
show here that they do have the geometric property that these rank loci are
constructible subvarieties. The same is true for loci defined by rank functions
in Schofield's subrepresentation bundles on $\rep(Q, \alpha)$, and in quiver
Grassmannians.

3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess