Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterizing projective spaces on deformations of Hilbert schemes of
  K3 surfaces   We seek to characterize homology classes of Lagrangian projective spaces
embedded in irreducible holomorphic-symplectic manifolds, up to the action of
the monodromy group. This paper addresses the case of manifolds
deformation-equivalent to the Hilbert scheme of length-three subschemes of a K3
surface. The class of the projective space in the cohomology ring has
prescribed intersection properties, which translate into Diophantine equations.
Possible homology classes correspond to integral points on an explicit elliptic
curve; our proof entails showing that the only such point is two-torsion.

26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con