Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Fano variety of linear spaces contained in two odd-dimensional
  quadrics   In this paper we describe the geometry of the 2m-dimensional Fano manifold G
parametrizing (m-1)-planes in a smooth complete intersection Z of two quadric
hypersurfaces in the complex projective space P^{2m+2}, for m>0. We show that
there are exactly 2^{2m+2} distinct isomorphisms in codimension one between G
and the blow-up of P^{2m} at 2m+3 general points, parametrized by the 2^{2m+2}
distinct m-planes contained in Z, and describe these rational maps explicitly.
We also describe the cones of nef, movable and effective divisors of G, as well
as their dual cones of curves. Finally, we determine the automorphism group of
G. These results generalize to arbitrary even dimension the classical
description of quartic del Pezzo surfaces (m=1).

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The categories of this paper are: q-bio
1
The categories of this paper are: cs
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics