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On triangular (D>n)-actions on cyclic p-gonal Riemann surfaces

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A compact Riemann surface X of genus g > 1 which has a conformal automorphism ρ of prime order p such that the orbit space X/(ρ) is the Riemann sphere is called cyclic p-gonal. Exceptional points in the moduli space Mg of compact Riemann surfaces of genus g are unique surface classes whose full group of conformal automorphisms acts with a triangular signature. We study symmetries of exceptional points in the cyclic p-gonal locus in Mg for which Aut(X)/(ρ is a dihedral group Dn.
Słowa kluczowe
Rocznik
Strony
103--122
Opis fizyczny
Bibliogr. 23 poz., tab.
Twórcy
  • University of Gdańsk Institute of Mathematics Wita Stwosza 57, 80-952 Gdańsk, Poland
Bibliografia
  • [1] R.D.M. Accola, On the number of automorphisms of a dosed Riemann surface, Trans. Amer. Math. Soc. 131 (1968), 398-408.
  • [2] R.D.M. Accola, On cyclic trigonal Riemann surfaces, Trans. Amer. Math. Soc. 283 (1984) 2, 423-449.
  • [3] G.V. Belyi, On Galois extensions of maximal cyclotomic field, Math. USSR Izvestiya 14 (1980), 247-256.
  • [4] S.A. Broughton, E. Bujalance, A.F. Costa, J.M. Gamboa, G. Gromadzki, Symmetries of Accola-Maclachlan and Kulkami Surfaces, Proc. Amer. Math. Soc. 127 (1999), 637-646.
  • [5] E. Bujalance, F.J. Cirre, J.M. Gamboa, G. Gromadzki, Symmetry Types of Hype.re.l-liptic Riemann Surfaces, Memoires de la Societe Mathematique De France (2001).
  • [6] G. Castelnuevo, Sulle serie algebriche di gruppi di punti apparte.ne.nti ad una curve algebraica, Rend. R. Academia Lincei Ser. 5 XV (1906), (Memorie scelte p. 509).
  • [7] H.M. Farkas, I. Kra, Riemann Surfaces, Graduate Text in Mathematics, Springer-Verlag, New York, 1980.
  • [8] G. Gromadzki, On a Harnack-Natanzon Theorem for the family of real forms of Rie­mann surfaces, J. Pure Appl. Algebra 121 (1997), 253-269.
  • [9] A. Harnack, Uber die Vieltheiligkeit der ebenen algebraischen Kurven, Math. Ann. 10 (1876), 189-199.
  • [10] A. Hurwitz, Uber alebraische Gebilde mit eindeutigen Transformationen in sich, Math. Ann. 41 (1983).
  • [11] G.A. Jones, D. Singerman, P.D. Watson, Symmetries of quasiplatonic Riemann sur­faces, Rev. Mat. Iberoam. (to appear).
  • [12] A.M. Macbeath, The classification of non-Euclidean plane crystallographies groups, Canad. J. Math. 19 (1966), 1192-1205.
  • [13] A.M. Macbeath, Action of automorphisms of a compact Riemann surface on the first homology group, Bull. Lond. Math. Soc. 5 (1973), 103-108.
  • [14] A.M. Macbeath, On a theorem of Hurwitz, Proc. Glasgow Math. Assoc. 5 (1961), 90-96.
  • [15] C. Maclachlan, Smooth coverings of hyperelliptic surfaces, Quart. Journal of Math. Oxford 2 (1971), 117-123.
  • [16] D. Singerman, Symmetries of Riemann surfaces with large automorphism group, Math. Ann. 210 (1974), 17-32.
  • [17] D. Singerman, Non-Euclidean crystallographies groups and Riemann surfaces, Ph.D. Thesis, Univ. of Birmingham, 1969.
  • [18] D. Singerman, Finitely maximal Fuchsian groups, J. Lond. Math. Soc. (2) 6 (1972), 29-38.
  • [19] D. Singerman, The remarkable Accola-Maclachlan surfaces, [in:] Contemp. Math., vol. 629, Amer. Math. Soc, Providence, RI, 2014, pp. 315-322.
  • [20] E. Tyszkowska, Topological classification of conformal actions on cyclic p-gonal Rie­mann surfaces, Journal of Algebra 344 (2011), 296-312.
  • [21] E. Tyszkowska, A. Weaver, Exceptional points in the elliptic-hyperelliptic locus, J. Pure Appl. Algebra 212 (2008), 1415-1426.
  • [22] A. Weaver, Hyperelliptic surfaces and their moduli, Geom. Dedicata 103 (2004), 69-87.
  • [23] H.C. Wilkie, On non-Euclidean crystallographic groups, Math. Z. 91 (1966), 87-102.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-e01e72e1-e68f-4397-bc73-8d9fbdf769a5
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