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 |
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| Date: | 2013 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2013
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/149354 |
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| 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| _version_ | 1862733307342487552 |
|---|---|
| author | Giavedoni, P. |
| author_facet | Giavedoni, P. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-12-07T19:37:03Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-149354 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T19:37:03Z |
| publishDate | 2013 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Giavedoni, P. 2019-02-21T07:09:45Z 2019-02-21T07:09:45Z 2013 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. 1815-0659 2010 Mathematics Subject Classification: 14P05; 57S30; 11F46 DOI: http://dx.doi.org/10.3842/SIGMA.2013.062 https://nasplib.isofts.kiev.ua/handle/123456789/149354 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. Research supported by SISSA under the PhD program in Mathematics and by the Austrian
 Science Fund (FWF) under Grant No. Y330. The author wishes to thank Professor Boris
 Dubrovin for kindly supervising this work and Professor Tamara Grava for valuable discussions.
 He also thanks the anonymous referees for significantly contributing to improve this article. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Period Matrices of Real Riemann Surfaces and Fundamental Domains Article published earlier |
| spellingShingle | Period Matrices of Real Riemann Surfaces and Fundamental Domains Giavedoni, P. |
| title | Period Matrices of Real Riemann Surfaces and Fundamental Domains |
| title_full | Period Matrices of Real Riemann Surfaces and Fundamental Domains |
| title_fullStr | Period Matrices of Real Riemann Surfaces and Fundamental Domains |
| title_full_unstemmed | Period Matrices of Real Riemann Surfaces and Fundamental Domains |
| title_short | Period Matrices of Real Riemann Surfaces and Fundamental Domains |
| title_sort | period matrices of real riemann surfaces and fundamental domains |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149354 |
| work_keys_str_mv | AT giavedonip periodmatricesofrealriemannsurfacesandfundamentaldomains |