On an algebraization of the Riemann-Hurwitz relation
The author studies the canonical representation Aut(M)\(\to GL(g,C)\) with the space of holomorphic differentials on M as its representation module, where M is a compact Riemann surface of genus\(\geq 2\). For an automorphism group AG of M, let R(M,AG) be its image. The GL(g,C)-conjugate class of R(M,AG) appears as an invariant of the holomorphic family of Riemann surfaces which is defined by the subgroup of Teichmüller modular group corresponding to the pair (M,AG). In this paper the author proves two necessary conditions for a finite subgroup of GL(g,C) to be conjugate to some R(M,AG). When \(g=2\) they are also sufficient conditions.
scientific article; zbMATH DE number 3918810
scientific article