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URN to cite this document: urn:nbn:de:bvb:703-epub-8877-1
Title data
Fallucca, Federico ; Gleißner, Christian ; Ruhland, Noah:
On rigid varieties isogenous to a product of curves.
In: Journal of Algebra.
Vol. 688
(2026)
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- pp. 393-419.
ISSN 1090-266X
DOI der Verlagsversion: https://doi.org/10.1016/j.jalgebra.2025.09.016
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Abstract
In this note, we study rigid complex manifolds that are realized as quotients of a product of curves by a free action of a finite group. They serve as higher-dimensional analogues of Beauville surfaces. Using uniformization, we outline the theory to characterize these manifolds through specific combinatorial data associated with the group under the assumption that the action is diagonal and the manifold is of general type. This leads to the notion of a n-fold Beauville structure. We define an action on the set of all n-fold Beauville structures of a given finite group that allows us to distinguish the biholomorphism classes of the underlying rigid manifolds. As an application, we give a classification of these manifolds with group Z52 in the three dimensional case and prove that this is the smallest possible group that allows a rigid, free and diagonal action on a product of three curves. In addition, we provide the classification of rigid 3-folds X given by a group acting faithfully on each factor for any value of the holomorphic Euler number χ(OX)≥−5.
Further data
| Item Type: | Article in a journal |
|---|---|
| Keywords: | Beauville surface; Beauville group; variety isogenous to a product of curves; Rigid complex manifold |
| DDC Subjects: | 500 Science > 510 Mathematics |
| Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics VIII - Complex Analysis and Differential Geometry Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics |
| Language: | English |
| Originates at UBT: | Yes |
| URN: | urn:nbn:de:bvb:703-epub-8877-1 |
| Date Deposited: | 10 Feb 2026 14:55 |
| Last Modified: | 10 Feb 2026 14:55 |
| URI: | https://epub.uni-bayreuth.de/id/eprint/8877 |
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