An infinite family of 2-groups with mixed Beauville structures

Barker, N.; Boston, N.; Peyerimhoff, N.; Vdovina, A.

Abstract

We construct an infinite family of triples (Gk, Hk, Tk), where Gk are 2-groups of increasing order, Hk are index 2 subgroups of Gk, and Tk are pairs of generators of Hk. We show that the triples uk = (Gk, Hk, Tk) are mixed Beauville structures if k is not a power of 2. This is the first known infinite family of 2-groups admitting mixed Beauville structures. Moreover, the associated Beauville surface S(u3) is real and, for k> 3 not a power of 2, the Beauville surface S(uk) is not biholomorphic to S(uk).

Citation

Barker, N., Boston, N., Peyerimhoff, N., & Vdovina, A. (2015). An infinite family of 2-groups with mixed Beauville structures. International Mathematics Research Notices, 2015(11), 3598-3618. https://doi.org/10.1093/imrn/rnu045

• Journal Article Type: Article
• Acceptance Date: Feb 26, 2014
• Online Publication Date: Mar 27, 2014
• Publication Date: Nov 1, 2015
• Deposit Date: Feb 27, 2014
• Publicly Available Date: Jun 17, 2014
• Journal: International Mathematics Research Notices
• Print ISSN: 1073-7928
• Electronic ISSN: 1687-0247
• Publisher: Oxford University Press
• Peer Reviewed: Peer Reviewed
• Volume: 2015
• Issue: 11
• Pages: 3598-3618
• DOI: https://doi.org/10.1093/imrn/rnu045
• Public URL: https://durham-repository.worktribe.com/output/1468479