Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cubic hypersurfaces with positive dual defects   We show that if a cubic hypersurface with positive dual defect over the
complex number field is not a cone, then either the hypersurface coincides with
the secant variety of the singular locus, or the hypersurface contains a linear
subvariety of dimension greater than the dual defect such that the intersection
of the singular locus and a general contact locus is contained in the linear
subvariety.

8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs