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arXiv · 1912.09973

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

Ingrid Bauer·Christian Gleissner
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Abstract

For each $n \geq 3$ the authors provide an $n$-dimensional rigid compact complex manifold of Kodaira dimension $1$. First they construct 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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Ingrid Bauer, Christian Gleissner. 2019-12-20. Fermat's Cubic, Klein's Quartic and Rigid Complex Manifolds of Kodaira Dimension One. https://arxiv.org/abs/1912.09973

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