Klein's Fundamental 2-Form of Second Kind for the Cab Curves
In this paper, we derive the exact formula of Klein's fundamental 2-form of second kind for the so-called Cab curves. The problem was initially solved by Klein in the 19th century for the hyper-elliptic curves, but little progress had been seen for its extension for more than 100 years. Recentl...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2017 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2017
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148579 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Klein's Fundamental 2-Form of Second Kind for the Cab Curves / J. Suzuki // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 18 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862726890830168064 |
|---|---|
| author | Suzuki, J. |
| author_facet | Suzuki, J. |
| citation_txt | Klein's Fundamental 2-Form of Second Kind for the Cab Curves / J. Suzuki // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 18 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In this paper, we derive the exact formula of Klein's fundamental 2-form of second kind for the so-called Cab curves. The problem was initially solved by Klein in the 19th century for the hyper-elliptic curves, but little progress had been seen for its extension for more than 100 years. Recently, it has been addressed by several authors, and was solved for subclasses of the Cab curves whereas they found a way to find its individual solution numerically. The formula gives a standard cohomological basis for the curves, and has many applications in algebraic geometry, physics, and applied mathematics, not just analyzing sigma functions in a general way.
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| first_indexed | 2025-12-07T19:00:06Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148579 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T19:00:06Z |
| publishDate | 2017 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Suzuki, J. 2019-02-18T16:12:24Z 2019-02-18T16:12:24Z 2017 Klein's Fundamental 2-Form of Second Kind for the Cab Curves / J. Suzuki // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 18 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 14H42; 14H50; 14H55 DOI:10.3842/SIGMA.2017.017 https://nasplib.isofts.kiev.ua/handle/123456789/148579 In this paper, we derive the exact formula of Klein's fundamental 2-form of second kind for the so-called Cab curves. The problem was initially solved by Klein in the 19th century for the hyper-elliptic curves, but little progress had been seen for its extension for more than 100 years. Recently, it has been addressed by several authors, and was solved for subclasses of the Cab curves whereas they found a way to find its individual solution numerically. The formula gives a standard cohomological basis for the curves, and has many applications in algebraic geometry, physics, and applied mathematics, not just analyzing sigma functions in a general way. The author would like to thank the anonymous referees. The discussion with them was very
 helpful for publishing this paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Klein's Fundamental 2-Form of Second Kind for the Cab Curves Article published earlier |
| spellingShingle | Klein's Fundamental 2-Form of Second Kind for the Cab Curves Suzuki, J. |
| title | Klein's Fundamental 2-Form of Second Kind for the Cab Curves |
| title_full | Klein's Fundamental 2-Form of Second Kind for the Cab Curves |
| title_fullStr | Klein's Fundamental 2-Form of Second Kind for the Cab Curves |
| title_full_unstemmed | Klein's Fundamental 2-Form of Second Kind for the Cab Curves |
| title_short | Klein's Fundamental 2-Form of Second Kind for the Cab Curves |
| title_sort | klein's fundamental 2-form of second kind for the cab curves |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148579 |
| work_keys_str_mv | AT suzukij kleinsfundamental2formofsecondkindforthecabcurves |