Real structures on torus bundles and their deformations

Fabrizio Catanese; Paola Frediani

Real structures on torus bundles and their deformations

Complex Variables 2007-05-23 v1 Algebraic Geometry

Authors: Fabrizio Catanese , Paola Frediani

Abstract

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.

Keywords

algebraic tori vector bundles bundle theory

Cite

@article{arxiv.math/0601108,
  title  = {Real structures on torus bundles and their deformations},
  author = {Fabrizio Catanese and Paola Frediani},
  journal= {arXiv preprint arXiv:math/0601108},
  year   = {2007}
}

Comments

26 pages, to appear in the Proceedings for 10th anniversary (2004) conference of the East China Normal University (Shanghai), published by AMS and Int. Press

Real structures on torus bundles and their deformations

Abstract

Keywords

Cite

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