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Quasiplatonic curves with symmetry group Z(2)(2) x Z(m) are definable over Q
University of La Frontera, Chile.
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
University of La Frontera, Chile.
University of La Frontera, Chile.
2017 (English)In: Bulletin of the London Mathematical Society, ISSN 0024-6093, E-ISSN 1469-2120, Vol. 49, no 1, 165-183 p.Article in journal (Refereed) Published
Abstract [en]

It is well known that every closed Riemann surface S of genus g amp;gt;= 2, admitting a group G of conformal automorphisms so that S/G has triangular signature, can be defined over a finite extension of Q. It is interesting to know, in terms of the algebraic structure of G, if S can in fact be defined over Q. This is the situation if G is either abelian or isomorphic to A x Z(2), where A is an abelian group. On the other hand, as shown by Streit and Wolfart, if G congruent to Z(p) x Z(q), where p, q amp;gt; 3 are prime integers, then S is not necessarily definable over Q. In this paper, we observe that if G congruent to Z(2)(2) x Z(m) with m amp;gt;= 3, then S can be defined over Q. Moreover, we describe explicit models for S, the corresponding groups of automorphisms, and an isogenous decomposition of their Jacobian varieties as product of Jacobians of hyperelliptic Riemann surfaces.

Place, publisher, year, edition, pages
WILEY , 2017. Vol. 49, no 1, 165-183 p.
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:liu:diva-136893DOI: 10.1112/blm.12014ISI: 000398892300015OAI: oai:DiVA.org:liu-136893DiVA: diva2:1092061
Note

Funding Agencies|Fondecyt Project [1150003]; Postdoctoral Fondecyt Projects [3160002, 3140050]; Beca Chile Fellowship for Postdoctoral Research; Project Anillo ACT PIA-CONICYT [1415]

Available from: 2017-04-29 Created: 2017-04-29 Last updated: 2017-04-29

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
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More languages
Output format
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