Stable vector bundles on generalized Kummer varieties

AbstractFor an abelian surfaceA, we explicitly construct two new families of stable vector bundles on the generalized Kummer varietyKn⁢(A){K_{n}(A)}forn⩾2{n\geqslant 2}. The first is the family of tautological bundles associated to stable bundles onA, and the second is the family of the “wrong-way” fibers of a universal family of stable bundles on the dual abelian surfaceA^{\widehat{A}}parametrized byKn⁢(A){K_{n}(A)}. Each family exhibits a smooth connected component in the moduli space of stable bundles onKn⁢(A){K_{n}(A)}, which is holomorphic symplectic but not simply connected, contrary to the case of K3 surfaces.