Michal Kapustka

Title: K3^[2] type IHS fourfolds with automorphisms
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Abstract:
We shall investigate the classification of IHS fourfolds of K3^[2] type
with automorphisms.
A classification of such manifolds in terms of lattices left invariant by
the automorhism were performed by Boissiere, Camere and Sarti. A geometric
realization of most cases have been constructed by Mongardi and Wandel as
so-called induced automorphisms or as degenerations of EPW sextics.
We complete the classifiaction by providing geometric realisations of
maximal dimensional families of IHS fourfolds of K3^[2]​ type with
involutions having invariant lattices: U(2), U(2)+E_8(-2) and
U(2)+D_4(-1). To do that, we exploit the construction of double EPW
quartic sections which are obtained as singular loci of special double EPW
cubes constructed in our earlier works.
The first part of the talk is joint work with Iliev, G. Kapustka, Ranestad
and the second with Camere, G. Kapustka and Mongardi.