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

  • Ingrid Bauer

    Mathematisches Institut, Universität Bayreuth, 95440 Bayreuth, Germany
  • Christian Gleissner

    Mathematisches Institut, Universität Bayreuth, 95440 Bayreuth, Germany
Fermat's Cubic, Klein's Quartic and Rigid Complex Manifolds of Kodaira Dimension One cover
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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