Absolutely trianalytic tori in Kummer variety

Let Z \subset M be a closed subset of a hyperkähler manifold. It is called trianalytic, if it is complex analytic with respect to I, J, K. It is known that there no trianalytic tori in the Hilbert schemes of K3 and O'Grady examples. In this talk i try to explain obstructions for the existence for trianalytic tori in the generalized Kummer variety.