Fermat's Cubic, Klein's Quartic and Rigid Complex Manifolds of Kodaira Dimension One
Doc. Math. 25, 1241-1262 (2020)
DOI: 10.25537/dm.2020v25.1241-1262
Communicated by Thomas Peternell
Summary
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.
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Affiliation
Bauer, Ingrid
Mathematisches Institut, Universität Bayreuth, 95440 Bayreuth, Germany
Gleissner, Christian
Mathematisches Institut, Universität Bayreuth, 95440 Bayreuth, Germany
