Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: EPW sextics and Hilbert squares of K3 surfaces   We prove that the Hilbert square $S^{[2]}$ of a very general primitively
polarized K3 surface S of degree $d(n) = 2(4n^2 + 8n + 5)$, $n \geq 1$ is
birational to a double Eisenbud-Popescu-Walter sextic. Our result implies a
positive answers, in the case when $r$ is even, to a conjecture of O'Grady: On
the Hilbert square of a very general K3 surface of genus $r^2 + 2$, $r \geq 1$
there is an antisymplectic involution. We explicitly give this involution on
$S^{[2]}$ in term of the corresponding EPW polarization on it.

1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex