Elliptic-Hyperelliptic Klein Surfaces With Many Automorphisms

Abstract

The authors establish that an elliptic-hyperelliptic Klein surface of genus p > 5 generically has at most 4(p-1)automorphisms, excepting the case X is orientable with 2 or 4 boundary components. If X is orientable with 2 or 4 boundary components the authors describe the structure of the group of automorhisms. They also prove that if X is an orientable elliptic-hyperelliptic Klein surface of genus p > 5 with 2 or 4 boundary components then the Teichm¨uller subset associated with X is a submanifold of dimension 1 of the Teichm¨uller space associated with X. The results obtained improve the evaluations formerly obtained by C. L. May [Pac. J. Math. 59, 199-210 (1975; Zbl 0422.30037)].