The number of isomorphism classes of Beauville surfaces with Beauville p-group

Date

2026-09-15

Author

Gül Erdem, Şükran

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A Beauville surface is a rigid complex surface of general type, isogenous to a higher product by the free action of a finite group G, called a Beauville group. In [22], González-Diez and Torres-Teigell find the number of isomorphism classes of Beauville surfaces for which the group G is PSL(2,p) with particular types of ‘Beauville structures’. On the other hand, in [21], González-Diez, Jones and Torres-Teigell give an explicit formula for this number when the group G is abelian. To the best of the author's knowledge, in the literature, the exact number of isomorphism classes of Beauville surfaces is given only for PSL(2,p) and for abelian groups. In this paper, we extend the result for Beauville surfaces with abelian p-group to Beauville surfaces for which the Beauville group is either a non-abelian metacyclic p-group or a p-group of nilpotency class 2.

Subject Keywords

Beauville groups, Beauville surfaces, Metacyclic p-groups, p-groups of class 2

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https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=105037750502&origin=inward
https://hdl.handle.net/11511/119305

Collections

Department of Mathematics, Article