Adapted hyperbolic polygons and symplectic representations for group actions on Riemann surfaces (Q1946177)

The goal of the paper is to provide an algorithm to construct a symplectic representation for the action of a group \(G\) on a Riemann surface \(M\) of genus \(g\geq 2\) such that the quotient surface \(M/G\) has genus zero. The fixed point set of this representation in the Siegel upper half-plane corresponds to a component of the singular locus of the moduli space of principally polarized abelian varieties. This component is described in terms of period matrices that may be explicitely computed from a marked set of generators of \(G\).