Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Singularities of 1/2 Calabi-Yau 4-folds and classification scheme for
  gauge groups in four-dimensional F-theory   In a previous study, we constructed a family of elliptic Calabi-Yau 4-folds
possessing a geometric structure that allowed them to be split into a pair of
rational elliptic 4-folds. In the present study, we introduce a method of
classifying the singularity types of this class of elliptic Calabi-Yau 4-folds.
In brief, we propose a method to classify the non-Abelian gauge groups formed
in four-dimensional (4D) $N=1$ F-theory for this class of elliptic Calabi-Yau
4-folds. To demonstrate our method, we explicitly construct several elliptic
Calabi-Yau 4-folds belonging to this class and study the 4D F-theory thereupon.
These constructions include a 4D model with two U(1) factors.

2
The categories of this paper are: math
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph