Examples of non-rigid, modular vector bundles on hyperkähler manifolds

We exhibit examples of slope-stable and modular vector bundles on a hyperkähler manifold of K3${}^{[2]}$-type which move in a 20-dimensional family and study their algebraic properties. These are obtained by performing standard linear algebra constructions on the examples studied by O’Grady of (rigid) modular bundles on the Fano varieties of lines of a general cubic 4-fold and the Debarre-Voisin hyperkähler manifold.