Examples of Non-Rigid, Modular Vector Bundles on Hyperkähler Manifolds

Abstract 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 four-fold and the Debarre–Voisin hyperkähler manifold.