Real structures on torus bundles and their deformations
Fabrizio Catanese, Paola Frediani
Abstract
We describe the family of real structures σ 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, σ) 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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