Grigorchuk–Gupta–Sidki groups as a source for Beauville surfaces

Abstract

If G is a Grigorchuk–Gupta–Sidki group defined over a p -adic tree, where p is an odd prime, we study the existence of Beauville surfaces associated to the quotients of G by its level stabilizers \mathrm {st}_G(n) . We prove that if G is periodic then the quotients G/\mathrm {st}_G(n) are Beauville groups for every n\geq 2 if p\geq 5 and n\geq 3 if p = 3 . In this case, we further show that all but finitely many quotients of G are Beauville groups. On the other hand, if G is non-periodic, then none of the quotients G/\mathrm {st}_G(n) are Beauville groups.

Locations

• arXiv (Cornell University) - View - PDF
• Communities in ADDI (University of the Basque Country) - View - PDF
• Groups Geometry and Dynamics - View