Real structures on torus bundles and their deformations

Details Real structures on torus bundles and their deformations Real structures on torus bundles and their deformations

2006-01-05

arxiv.org/abs/math/0601108v1

Mathematics

Complex Variables

26 pages, to appear in the Proceedings for 10th anniversary (2004) conference of the East China Normal University (Shanghai),

Scientific paper

We describe the family of real structures $\sigma$ on principal holomorphic torus bundles $X$ over tori, and prove its connectedness when the complex dimension is at most three. From this and previous results of the authors follows that the differentiable type (more precisely, the orbifold fundamental group) determines the deformation type of the pair $(X, \sigma)$ provided we have complex dimension at most three, fibre dimension one, and a certain 'reality' condition on the fundamental group is satisfied.

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