| Title: |
On rigid varieties isogenous to a product of curves |
| Authors: |
Fallucca F.; Gleissner C.; Ruhland N. |
| Contributors: |
Fallucca, F; Gleissner, C; Ruhland, N |
| Publisher Information: |
Academic Press Inc.; US |
| Publication Year: |
2026 |
| Collection: |
Università degli Studi di Milano-Bicocca: BOA (Bicocca Open Archive) |
| Subject Terms: |
Beauville group; variety isogenous to a product of curve; Beauville surface; Rigid complex manifold; Settore MATH-02/B - Geometria |
| Description: |
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. |
| Document Type: |
article in journal/newspaper |
| File Description: |
STAMPA |
| Language: |
English |
| Relation: |
info:eu-repo/semantics/altIdentifier/wos/WOS:001603005700005; volume:688; issue:15 February 2026; firstpage:393; lastpage:419; numberofpages:27; journal:JOURNAL OF ALGEBRA; https://hdl.handle.net/10281/573182 |
| DOI: |
10.1016/j.jalgebra.2025.09.016 |
| Availability: |
https://hdl.handle.net/10281/573182; https://doi.org/10.1016/j.jalgebra.2025.09.016 |
| Rights: |
info:eu-repo/semantics/openAccess ; license:Creative Commons ; license uri:http://creativecommons.org/licenses/by/4.0/ |
| Accession Number: |
edsbas.9F97F1A1 |
| Database: |
BASE |