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

GÜL ERDEM Ş.

Journal of Algebra, cilt.702, ss.176-209, 2026 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 702
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1016/j.jalgebra.2026.05.002
  • Dergi Adı: Journal of Algebra
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.176-209
  • Anahtar Kelimeler: Beauville groups, Beauville surfaces, Metacyclic p-groups, p-groups of class 2
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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.