Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the loci of morphisms from $\mathbb{P}^1$ to $G(r,n)$ with fixed
  splitting type of the restricted universal sub-bundle or quotient bundle   Let $n\geq 4$, $2 \leq r \leq n-2$ and $e \geq 1$. We show that the
intersection of the locus of degree $e$ morphisms from $\mathbb{P}^1$ to
$G(r,n)$ with the restricted universal sub-bundles having a given splitting
type and the locus of degree $e$ morphisms with the restricted universal
quotient-bundle having a given splitting type is non-empty and generically
transverse. As a consequence, we get that the locus of degree $e$ morphisms
from $\mathbb{P}^1$ to $G(r,n)$ with the restricted tangent bundle having a
given splitting type need not always be irreducible.

19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th