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arXiv · 2212.05859

On Rigid Manifolds of Kodaira Dimension 1

Ingrid Bauer·Christian Gleissner·Julia Kotonski
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Abstract

We discuss rigid compact complex manifolds of Kodaira dimension 1, arising as product-quotient varieties. First, we show that there is no free rigid action on the product of $(n-1)$ elliptic curves and a curve of genus at least two. Then, we describe the occurring groups, study the quotients and prove that there is always a suitable resolution of singularities preserving rigidity. Finally, we give a complete classification of the cases arising for minimal group orders.

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Ingrid Bauer, Christian Gleissner, Julia Kotonski. 2022-12-12. On Rigid Manifolds of Kodaira Dimension 1. https://arxiv.org/abs/2212.05859

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