# Period Matrices of Real Riemann Surfaces and Fundamental Domains

@article{Giavedoni2013PeriodMO, title={Period Matrices of Real Riemann Surfaces and Fundamental Domains}, author={Pietro Giavedoni}, journal={Symmetry Integrability and Geometry-methods and Applications}, year={2013}, volume={9}, pages={062} }

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…

## 2 Citations

### A degeneration of two-phase solutions of focusing NLS via Riemann-Hilbert problems

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Two-phase solutions of focusing NLS equation are classically constructed out of an appropriate Riemann surface of genus two, and expressed in terms of the corresponding theta-function. We show here…

### A degeneration of two-phase solutions of the focusing nonlinear Schrödinger equation via Riemann-Hilbert problems

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- 2015

Two-phase solutions of focusing NLS equation are classically constructed out of an appropriate Riemann surface of genus two and expressed in terms of the corresponding theta-function. We show here…

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