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SIGMA, 2017, Volume 13, 017, 13 pages (Mi sigma1217)  

This article is cited in 2 scientific papers (total in 2 papers)

Klein's Fundamental $2$-Form of Second Kind for the $C_{ab}$ Curves

Joe Suzuki

Department of Mathematics, Osaka University, Machikaneyama Toyonaka, Osaka 560-0043, Japan

Abstract: In this paper, we derive the exact formula of Klein's fundamental $2$-form of second kind for the so-called $C_{ab}$ 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 $C_{ab}$ 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.

Keywords: $C_{ab}$ curves; Klein's fundamental $2$-form of second kind; cohomological basis; symmetry.

DOI: https://doi.org/10.3842/SIGMA.2017.017

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Full text: http://www.emis.de/.../017
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Bibliographic databases:

ArXiv: 1701.00931
MSC: 14H42; 14H50; 14H55
Received: January 5, 2017; in final form March 11, 2017; Published online March 16, 2017
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Citation: Joe Suzuki, “Klein's Fundamental $2$-Form of Second Kind for the $C_{ab}$ Curves”, SIGMA, 13 (2017), 017, 13 pp.

Citation in format AMSBIB
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\by Joe~Suzuki
\paper Klein's Fundamental $2$-Form of Second Kind for the $C_{ab}$ Curves
\jour SIGMA
\yr 2017
\vol 13
\papernumber 017
\totalpages 13
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\crossref{https://doi.org/10.3842/SIGMA.2017.017}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85016055510}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. D. V. Leikin, Yu. N. Bernatskaya, “On Regularization of Second Kind Integrals”, SIGMA, 14 (2018), 074, 28 pp.  mathnet  crossref
    2. Komeda J., Matsutani Sh., Previato E., “The SIGMA Function For Trigonal Cyclic Curves”, Lett. Math. Phys., 109:2 (2019), 423–447  crossref  mathscinet  zmath  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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