The Ramificant Determinant
We give an introduction to the transalgebraic theory of simply connected log-Riemann surfaces with a finite number of infinite ramification points (transalgebraic curves of genus 0). We define the base vector space of transcendental functions and establish, by elementary methods, some transcendental...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2019 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2019
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/210302 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | The Ramificant Determinant / K. Biswas, R. Pérez-Marco // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 19 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862686563690872832 |
|---|---|
| author | Biswas, K. Pérez-Marco, R. |
| author_facet | Biswas, K. Pérez-Marco, R. |
| citation_txt | The Ramificant Determinant / K. Biswas, R. Pérez-Marco // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 19 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We give an introduction to the transalgebraic theory of simply connected log-Riemann surfaces with a finite number of infinite ramification points (transalgebraic curves of genus 0). We define the base vector space of transcendental functions and establish, by elementary methods, some transcendental properties. We introduce the Ramificant determinant constructed with transcendental periods, and we give a closed-form formula that gives the main applications to transalgebraic curves. We prove an Abel-like theorem and a Torelli-like theorem. Transposing to the transalgebraic curve, the base vector space of transcendental functions, they generate the structural ring from which the points of the transalgebraic curve can be recovered algebraically, including infinite ramification points.
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| first_indexed | 2025-12-07T21:25:04Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210302 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T21:25:04Z |
| publishDate | 2019 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Biswas, K. Pérez-Marco, R. 2025-12-05T09:27:25Z 2019 The Ramificant Determinant / K. Biswas, R. Pérez-Marco // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 19 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 30F99; 30D99 arXiv: 1903.06770 https://nasplib.isofts.kiev.ua/handle/123456789/210302 https://doi.org/10.3842/SIGMA.2019.086 We give an introduction to the transalgebraic theory of simply connected log-Riemann surfaces with a finite number of infinite ramification points (transalgebraic curves of genus 0). We define the base vector space of transcendental functions and establish, by elementary methods, some transcendental properties. We introduce the Ramificant determinant constructed with transcendental periods, and we give a closed-form formula that gives the main applications to transalgebraic curves. We prove an Abel-like theorem and a Torelli-like theorem. Transposing to the transalgebraic curve, the base vector space of transcendental functions, they generate the structural ring from which the points of the transalgebraic curve can be recovered algebraically, including infinite ramification points. We are grateful to Y. Levagnini and the referees for their careful reading and corrections that improved the article. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Ramificant Determinant Article published earlier |
| spellingShingle | The Ramificant Determinant Biswas, K. Pérez-Marco, R. |
| title | The Ramificant Determinant |
| title_full | The Ramificant Determinant |
| title_fullStr | The Ramificant Determinant |
| title_full_unstemmed | The Ramificant Determinant |
| title_short | The Ramificant Determinant |
| title_sort | ramificant determinant |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210302 |
| work_keys_str_mv | AT biswask theramificantdeterminant AT perezmarcor theramificantdeterminant AT biswask ramificantdeterminant AT perezmarcor ramificantdeterminant |