Real Structures on Marked Schottky Space

Abstract

Marked Schottky space M S g is an explicit model of the quasiconformal deformation space of a Schottky group of rank g , this being isomorphic to the punctured unit disc for g = 1 and, for g ⩾ 2 , a connected complex manifold of dimension 3 ( g − 1 ) . This space is an intermediate non‐Galois cover of moduli space of genus g curves. In this paper we provide a description of the real structures of M S g , up to holomorphic automorphisms, together with their real parts.

Marked Schottky space M S g is an explicit model of the quasiconformal deformation space of a Schottky group of rank g , this being isomorphic to the punctured unit disc for g = 1 and, for g ⩾ 2 , a connected complex manifold of dimension 3 ( g − 1 ) . This space is an intermediate non‐Galois cover of moduli space of genus g curves. In this paper we provide a description of the real structures of M S g , up to holomorphic automorphisms, together with their real parts.