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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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2017
1. Verfasser: Suzuki, J.
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2017
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/148579
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren: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
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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.
first_indexed 2025-12-07T19:00:06Z
format Article
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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