More on Strongly Real Beauville Groups
نویسنده
چکیده
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.
منابع مشابه
A new infinite family of non-abelian strongly real Beauville p-groups for every odd prime p
We explicitly construct infinitely many a non-abelian strongly real Beauville p-groups for every prime p. Until very recently only finitely many non-abelian strongly real Beauville p-groups were known and all of these were 2-groups.
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We generalize earlier work of Fuertes and González-Diez as well as earlier work of Bauer, Catanese and Grunewald by classifying which of the irreducible Coxeter groups are (strongly real) Beauville groups. We also make partial progress on the much more difficult question of which Coxeter groups are Beauville groups in general as well as discussing the related question of which Coxeter groups ca...
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متن کاملNew examples of mixed Beauville groups
We generalise a construction of mixed Beauville groups first given by Bauer, Catanese and Grunewald. We go on to give several examples of infinite families of characteristically simple groups that satisfy the hypotheses of our theorem and thus provide a wealth of new examples of mixed Beauville groups.
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تاریخ انتشار 2015