Lagrangian fibrations on Nikulin orbifold

The geometry of irreducible holomorphic symplectic (IHS, sometimes referred to as hyperkähler) manifolds can be studied through the numerical properties of algebraic classes with respect to a non-degenerate quadratic form on the second cohomology group. In this context, a famous conjecture (SYZ) predicts that the existence of Lagrangian fibrations is detected by the presence of certain isotropic classes. While the conjecture holds in all known examples, it remains open in general. Recently, singular analogues of IHS manifolds have been proposed, providing a new framework to test the conjecture in a singular setting. In this talk, I will focus on Nikulin orbifolds, which are among the simplest singular examples, and present recent work classifying possible fibrations in this deformation class, from which the SYZ conjecture follows in this specific case.