Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dually degenerate varieties and the generalization of a theorem of
  Griffiths--Harris   The dual variety X* for a smooth n-dimensional variety X of the projective
space P^N is the set of tangent hyperplanes to X. In the general case, the
variety X* is a hypersurface in the dual space (P^N)*. If dim X* < N - 1, then
the variety X is called dually degenerate.
  The authors refine these definitions for a variety X \subset P^N with a
degenerate Gauss map of rank r. For such a variety, in the general case, the
dimension of its dual variety X* is N - l - 1, where l = n - r, and X is dually
degenerate if dim X* < N - l - 1.
  In 1979 Griffiths and Harris proved that a smooth variety X \subset P^N is
dually degenerate if and only if all its second fundamental forms are singular.
The authors generalize this theorem for a variety X \subset P^N with a
degenerate Gauss map of rank r.

35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph