Period Matrices of Real Riemann Surfaces and Fundamental Domains

For some positive integers g and n we consider a subgroup Gg,n of the 2g-dimensional modular group keeping invariant a certain locus Wg,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 on Wg,n. Our motivati...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2013
ISSN:1815-0659
Main Author: Giavedoni, P.
Format: Article
Language:English
Published: Інститут математики НАН України 2013
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/149354
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Period Matrices of Real Riemann Surfaces and Fundamental Domains / P. Giavedoni // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 22 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Summary:For some positive integers g and n we consider a subgroup Gg,n of the 2g-dimensional modular group keeping invariant a certain locus Wg,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 on Wg,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.
ISSN:1815-0659