Counter-example to global Torelli problem for irreducible symplectic manifolds

Details Counter-example to global Torelli problem for irreducible symplectic manifolds Counter-example to global Torelli problem for irreducible symplectic manifolds

2001-10-11

arxiv.org/abs/math/0110114v3

Mathematics

Algebraic Geometry

The main part does not change. But Remark 3 is not correct (Erratum is added at the end of the paper)

Scientific paper

We 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.

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