Period matrices of real Riemann surfaces and fundamental domains (Q2447833)

In the literature on Riemann surfaces, most of the results are related to those on hyperbolic space. In the paper under review, the author studies those Riemann surfaces acting on the Siegel upper half plane of degree \(g\), which is defined as the space of \(g\times g\) complex symmetric matrices whose imaginary part is positive definite. Every discrete group has a fundamental region. In this paper, a fundamental domain for the modular action of the subgroup on a certain locus. The geometric interpretation of Riemann surfaces is used in the proofs. It is a nice paper for those studying Riemann surfaces, algebraic geometry and discrete groups.