Purely (non-)strongly real Beauville p-groups
نویسندگان
چکیده
منابع مشابه
More on Strongly Real Beauville Groups
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 sur...
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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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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. In this survey we discuss the p-groups that may be used in this way. En route we discuss several open problems, questions and conjectures.
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We examine which p-groups of order ≤ p6 are Beauville. We completely classify them for groups of order ≤ p4. We also show that the proportion of 2-generated groups of order p5 which are Beauville tends to 1 as p tends to infinity; this is not true, however, for groups of order p6. For each prime p we determine the smallest non-abelian Beauville p-group.
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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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ژورنال
عنوان ژورنال: Archiv der Mathematik
سال: 2020
ISSN: 0003-889X,1420-8938
DOI: 10.1007/s00013-020-01441-8