2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62367We shall give an example of irreducible symplectic manifolds X and Y which are not bimeromorphic, but have the same periods in the second cohomologies. More explicitly, X and Y are generalized Kummer varieties of dim 4 for a general complex torus T of dim 2 and its dual torus T^*. A key result is an observation of Shioda for the periods of T and T^*. As a concluding remark, we shall discuss the difference between our case and Kummer surfaces.The main part does not change. But Remark 3 is not correct (Erratum is added at the end of the paper)Algebraic Geometrytext