Induced nonsymplectic automorphisms on manifolds of OG6 type

In 2000 O'Grady introduced a new example of hyperkaehler manifolds in dimension six as the symplectic resolution of a certain fiber of a moduli space of sheaves on an abelian surface. In this talk we give you a criterion to determine when a birational transformation of an O'Grady six type manifold is induced by an automorphism of the abelian surface. Using the lattice theoretic classi cation of nonsymplectic automorphisms of O'Grady's sixfolds we give an application of this criterion to detect when an automorphism is induced.