• DOI:10.3842/SIGMA.2013.062
• Corpus ID: 7143943

Period Matrices of Real Riemann Surfaces and Fundamental Domains

@article{Giavedoni2012PeriodMO,
  title={Period Matrices of Real Riemann Surfaces and Fundamental Domains},
  author={Pietro Giavedoni},
  journal={Symmetry Integrability and Geometry-methods and Applications},
  year={2012},
  volume={9},
  pages={062}
}

• Pietro Giavedoni
• Published 16 February 2012
• Mathematics
• Symmetry Integrability and Geometry-methods and Applications

For some positive integers g and n we consider a subgroup Gg;n of the 2g- dimensional modular group keeping invariant a certain locusWg;n in the Siegel upper half plane of degree g. We address the problem of describing a fundamental domain for the modular action of the subgroup onWg;n. Our motivation comes from geometry: g and n represent the genus and the number of ovals of a generic real Riemann surface of separated type; the locus Wg;n contains the corresponding period matrix computed with respect to some specific basis in the homology. In this paper we formulate a general procedure to solve the problem when g is even and n equals one. For g equal to two or four the explicit calculations are worked out in full detail.