On real forms of a Belyi action of the alternating groups

C. Bagiński , J. J. Etayo , Grzegorz Gromadzki , E. Martínez

Abstract

In virtue of the Belyi Theorem a complex algebraic curve can bedefined over the algebraic numbers if and only if the corresponding Riemannsurface can be uniformized by a subgroup of a Fuchsian triangle group. Suchsurfaces are known as Belyi surfaces. Here we study certain natural actionsof the alternating groupsAnon them. We show that they are symmetricand calculate the number of connected components, called ovals, of the corresponding real forms. We show that all symmetries with ovals are conjugateand we calculate the number of purely imaginary real forms both in case ofAnconsidered here andSnconsidered in an earlier paper.
Author C. Bagiński
C. Bagiński,,
-
, J. J. Etayo
J. J. Etayo,,
-
, Grzegorz Gromadzki (FMPI / IM)
Grzegorz Gromadzki,,
- Institute of Mathematics
, E. Martínez
E. Martínez,,
-
Journal seriesAlbanian Journal of Mathematics, ISSN , e-ISSN 1930-1235, (0 pkt)
Issue year2016
Vol10
No1
Pages3-10
Publication size in sheets0.5
Keywords in Englishautomorphisms of Riemann surfaces, Belyi actions of alternating groups, real forms of complex algebraic curves, ovals
URL http://albanian-j-math.com/archives/2016-01.pdf
Languageen angielski
Score (nominal)5
ScoreMinisterial score = 0.0, 24-07-2019, ArticleFromJournal
Ministerial score (2013-2016) = 5.0, 24-07-2019, ArticleFromJournal - czasopismo zagraniczne spoza list
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