Coxeter groups as Beauville groups

Fairbairn, Ben

doi:10.1007/s00605-015-0848-y

Cited by 2 publications

(2 citation statements)

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“…Another class of 2-generated finite groups that have only been partially investigated from the viewpoint of Beauville constructions are reflection groups. In [31] the author proves the following. Altogether the above goes most of the way to classifying which of the real reflection groups are strongly real Beauville groups, however completing the task is more difficult.…”

Section: Reflection Groupsmentioning

confidence: 82%

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Strongly Real Beauville Groups III

Fairbairn

2020

Springer Proceedings in Mathematics &Amp; Statistics

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Beauville surfaces are a class of complex surfaces defined by letting a finite group G act on a product of Riemann surfaces. These surfaces possess many attractive geometric properties several of which are dictated by properties of the group G. A particularly interesting subclass are the 'strongly real' Beauville surfaces that have an analogue of complex conjugation defined on them. In this survey we discuss these objects and in particular the groups that may be used to define them. En route we discuss several open problems, questions and conjectures and in places make some progress made on addressing these.

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Section: Reflection Groupsmentioning

confidence: 82%

“…Altogether the above goes most of the way to classifying which of the real reflection groups are strongly real Beauville groups, however completing the task is more difficult. Several examples are given in [31,Section 5] showing that K 1 × K 2 can be a strongly real Beauville group, even when K 1 and/or K 2 are not. Question 8.…”

Section: Reflection Groupsmentioning

confidence: 99%