Stable vector bundles on generalized Kummer varieties

Abstract

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