Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lattice duality for families of $K3$ surfaces associated to transpose
  duality   The aim of this article is to show that the transpose-dual pairs in the sense
of Ebeling-Ploog of singularities $(Z_{1,0},\, Z_{1,0})$, $(U_{1,0},\,
U_{1,0})$, $(Q_{17},\, Z_{2,0})$, $(W_{1,0},\, W_{1,0})$ that are concluded to
be polytope-dual by the author are actually lattice-dual.

27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg