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  • Wada dessins associated with finite projective spaces and Frobenius compatibility
    Sarti, Cristina
    Dessins d'enfants (hypermaps) are useful to describe algebraic properties of the Riemann surfaces they are embedded in. In general, it is not easy to describe algebraic properties of the surface of ... the embedding starting from the combinatorial properties of an embedded dessin. However, this task becomes easier if the dessin has a large automorphism group. In this paper we consider a special type of dessins, so-called Wada dessins. Their underlying graph illustrates the incidence structure of finite projective spaces ▫$\Bbb P^m (\Bbb F_n)$▫. Usually, the automorphism group of these dessins is a cyclic Singer group ▫$\Sigma _\ell$▫ permuting transitively the vertices. However, in some cases, a second group of automorphisms ▫$\Phi_f$▫ exists. It is a cyclic group generated by the Frobenius automorphism. We show under what conditions ▫$\Phi_f$▫ is a group of automorphisms acting freely on the edges of the considered dessins.
    Vir: Ars mathematica contemporanea. - ISSN 1855-3966 (Vol. 4, no. 2, 2011, str. 291-311)
    Vrsta gradiva - članek, sestavni del
    Leto - 2011
    Jezik - angleški
    COBISS.SI-ID - 16267865

    Povezava(-e):

    http://amc.imfm.si/index.php/amc/article/view/122
    Digitalna knjižnica Slovenije - dLib.si

vir: Ars mathematica contemporanea. - ISSN 1855-3966 (Vol. 4, no. 2, 2011, str. 291-311)

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