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Klein's Fundamental 2-Form of Second Kind for the Cab Curves
Репозиторій DSpace/Manakin
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2017, том 13
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Klein's Fundamental 2-Form of Second Kind for the Cab Curves
Інший ID:
2010 Mathematics Subject Classification: 14H42; 14H50; 14H55
DOI:10.3842/SIGMA.2017.017
DOI:10.3842/SIGMA.2017.017
Посилання:
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.
Підтримка:
The author would like to thank the anonymous referees. The discussion with them was very
helpful for publishing this paper.
Дата:
2017
Переглядів:
612
Завантажень:
248
Анотація:
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.
