Free dihedral actions on abelian varieties

  • Bruno Aguiló Vidal Departamento de Matemáticas, Facultad de Ciencias, Universidad de Chile, Las Palmeras 3425, Ñuñoa, Santiago, Chile.
Keywords: Abelian varieties, dihedral group, free action

Abstract

We give a simple construction for hyperelliptic varieties, defined as the quotient of a complex torus by the action of a finite group \(G\) that contains no translations and acts freely, with \(G\) any dihedral group. This generalizes a construction given by Catanese and Demleitner for \(D_4\) in dimension three.

References

R. Auffarth and G. Lucchini Arteche, “Smooth quotients of complex tori by finite groups”, Preprint (2021). arXiv:1912.05327.

F. Catanese and P. Corvaja, “Teichmüller spaces of generalized hyperelliptic manifolds”, Complex and symplectic geometry, Springer INdAM Ser. 21, Springer, Cham, 2017, pp. 39-49.

F. Catanese and A. Demleitner, “The classification of hyperelliptic threefolds”, Groups Geom. Dyn, vol. 14, no. 4, pp. 1447–1454, 2020.

F. Catanese and A. Demleitner, “Hyperelliptic threefolds with group D4, the dihedral group of order 8”, Preprint (2018), arXiv:1805.01835.

E. C. Mistretta, “Holomorphic symmetric differentials and parallelizable compact complex manifolds”, Riv. Math. Univ. Parma (N.S.), vol. 10, no. 1, pp. 187–197, 2019.

K. Uchida and H. Yoshihara, “Discontinuous groups of affine transformations of C3”. Tohoku Math. J. (2), vol. 28, no. 1, pp. 89–94, 1976.

Published
2021-08-01
How to Cite
[1]
B. Aguiló Vidal, “Free dihedral actions on abelian varieties”, CUBO, vol. 23, no. 2, pp. 239–244, Aug. 2021.
Section
Articles