Fermat's Cubic, Klein's Quartic and Rigid Complex Manifolds of Kodaira Dimension One

摘要

For each (n geq 3) we provide an (n)-dimensional rigid compact complex manifold of Kodaira dimension (1). First we constructed a series of singular quotients of products of ((n-1)) Fermat curves with the Klein quartic, which are rigid. Then using toric geometry a suitable resolution of singularities is constructed and the deformation theories of the singular model and of the resolutions are compared, showing the rigidity of the resolutions.