## On the automorphisms of double EPW sextics

Pietro Beri
Université de Poitiers (France)
Abstract:
EPW sextics are a family of hypersurfaces in the projective space of dimension
$5$
that admits a double cover;; this double cover is a deformation of the Hilbert square of a
$K3$
surface, and thus a hyperkahler fourfold. I will present some examples of automorphisms of double EPW sextics. I will then provide an overview of the link with Gushel- Mukai varieties, showed by A. Iliev, L. Manivel and O. Debarre, and I will present some work in progress about the latter construction.