Michał and Grzegorz Kapustka - Nikulin type orbifolds

We will discuss the recent theory of Nikulin orbifolds and orbifolds of Nikulin type in dimension 4. Nikulin orbifolds are irreducible holomorphic symplectic orbifolds which are partial resolutions of quotients of IHS manifolds of K3^[n] type. Their deformations are called orbifolds of Nikulin type. Our main aim will be the description of the first known locally complete family of projective irreducible holomorphic symplectic orbifolds of dimension 4 which are of Nikulin type. It is a family of IHS orbifolds that appear as double covers of special complete intersections (3,4) in P^6. This is joint work with Ch. Camere and A. Garbagnati.