Fermat's Cubic, Klein's Quartic and Rigid Complex Manifolds of Kodaira Dimension One
Ingrid Bauer
Mathematisches Institut, Universität Bayreuth, 95440 Bayreuth, GermanyChristian Gleissner
Mathematisches Institut, Universität Bayreuth, 95440 Bayreuth, Germany
Abstract
For each we provide an -dimensional rigid compact complex manifold of Kodaira dimension . First we constructed a series of singular quotients of products of 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.
Cite this article
Ingrid Bauer, Christian Gleissner, Fermat's Cubic, Klein's Quartic and Rigid Complex Manifolds of Kodaira Dimension One. Doc. Math. 25 (2020), pp. 1241–1262
DOI 10.4171/DM/775