Surfaces elliptiques-hyperelliptiques avec beaucoup d'automorphismes

  1. E. Bujalance
  2. J. M. Gamboa
  3. J. J. Etayo
Revista:
Comptes Rendus des Séances de l'Académie des Sciences. Série I. Mathématique

Año de publicación: 1986

Volumen: 302

Número: 10

Páginas: 391-394.

Tipo: Artículo

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Resumen

"C. L. Mayproved [Pacific J. Math. 59 (1975), no. 1, 199–210; MR0399451] that every Klein surface with boundary whose algebraic genus is p has at most 12(p−1) automorphisms. In this note we prove that the number of automorphisms of an elliptic-hyperelliptic Klein surface with genus p>5 is generically less than or equal to 4(p−1), except in the following cases: (i) X is orientable with 4 boundary components and in this case the group of automorphisms is (Dp−1×C2)⋊C2; and (ii) X is orientable with 2 boundary components and the group of automorphisms is D2(p−1)⋊C2. We also prove that the Teichmüller subset associated to these surfaces is a manifold.''