Recent work on Beauville surfaces, structures and groups

Fairbairn, Ben

doi:10.1017/cbo9781316227343.014

Cited by 14 publications

(19 citation statements)

References 66 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Slightly older surveys discussing related geometric and topological matters are given by Bauer, Catanese and Pignatelli in [10,11]. Other notable Ben Fairbairn Department of Economics, Mathematics and Statistics, Birkbeck, University of London, Malet Street, London, WC1E 7HX e-mail: b.fairbairn@bbk.ac.uk works in the area include [6,21,41,48,53]. Whilst this article is largely expository in nature we also report incremental progress on various different problems that will appear here.…”

Section: Introductionmentioning

confidence: 89%

More on Strongly Real Beauville Groups

Fairbairn

2016

Symmetries in Graphs, Maps, and Polytopes

Self Cite

View full text Add to dashboard Cite

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 discuss some progress made on addressing these.

show abstract

Section: Introductionmentioning

confidence: 89%

More on Strongly Real Beauville Groups

Fairbairn

2016

Symmetries in Graphs, Maps, and Polytopes

Self Cite

View full text Add to dashboard Cite

show abstract

“…Since G is of odd order, we have o(z 1 ) = 2. Then in this case we take T 1 = (z 2 1 , z −1 1 , z 2 , . .…”

Section: Finite Nilpotent Groupsmentioning

confidence: 99%

On ramification structures for finite nilpotent groups

Gül¹

2018

HJMS

View full text Add to dashboard Cite

We extend the characterization of abelian groups with ramification structures given by Garion and Penegini in [?] to finite nilpotent groups whose Sylow p-subgroups have a 'nice power structure', including regular p-groups, powerful p-groups and (generalized) p-central p-groups. We also correct two errors in [?] regarding abelian 2-groups with ramification structures and the relation between the sizes of ramification structures for an abelian group and those for its Sylow 2-subgroup.

show abstract

“…For G = P SL 2 (11) we have that a triple of type (p, q − , q − ) exists by [26] or alternatively the words ab and [a, b] in the standard generators for G [40] give an odd triple of type (11,5,5). In both cases we have, by Lemma 14, an odd triple of type or (55, 55, 5) for G × G. For our even triple, the structure constants for the number of triples of type (6,6,6) can be computed and is seen to be twice the order of Aut(G) and so we have an even triple for G and G × G. For G = P SL 2 (27) we take the words in the standard generators [40] (ab) 2 (abb) 2 , a b 2 which give an even triple of type (2,14,7) and the words b 2 , b a which give an odd triple of type (3,3,13). Again, by Lemma 14, these give a mixable Beauville structure on G × G. Finally, we remark that when q ≡ ±1 mod 4 we have that q − and q + have opposite parity and this determines the parity of our triples.…”

Section: 1mentioning

confidence: 99%