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More on Strongly Real Beauville Groups

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Symmetries in Graphs, Maps, and Polytopes (SIGMAP 2014)

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Abstract

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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Acknowledgments

The author wishes to express his deepest gratitude to the organisers of the 2014 installment of the conferences on Symmetries in Graphs, Maps, and Polytopes hosted by The Open University and in particular to Professor Jozef Širáň for making this publication possible. The author wishes to thank the anonymous referees for their lengthy and in-depth commentary they provided on this submission.

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Authors and Affiliations

  1. Department of Economics, Mathematics and Statistics, Birkbeck, University of London, Malet Street, London, WC1E 7HX, UK

    Ben Fairbairn

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  1. Ben Fairbairn
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Correspondence to Ben Fairbairn .

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Editors and Affiliations

  1. The Open University, Milton Keynes, United Kingdom

    Jozef Širáň

  2. Comenius University, Bratislava, Slovakia

    Robert Jajcay

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Fairbairn, B. (2016). More on Strongly Real Beauville Groups. In: Širáň, J., Jajcay, R. (eds) Symmetries in Graphs, Maps, and Polytopes. SIGMAP 2014. Springer Proceedings in Mathematics & Statistics, vol 159. Springer, Cham. https://doi.org/10.1007/978-3-319-30451-9_6

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