Counter-example to global Torelli problem for irreducible symplectic manifolds
Algebraic Geometry
2007-05-23 v3
Abstract
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.
Keywords
Cite
@article{arxiv.math/0110114,
title = {Counter-example to global Torelli problem for irreducible symplectic manifolds},
author = {Yoshinori Namikawa},
journal= {arXiv preprint arXiv:math/0110114},
year = {2007}
}
Comments
The main part does not change. But Remark 3 is not correct (Erratum is added at the end of the paper)