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Funktsional. Anal. i Prilozhen., 2000, Volume 34, Issue 3, Pages 1–16 (Mi faa307)  

This article is cited in 41 scientific papers (total in 43 papers)

Uniformization of Jacobi Varieties of Trigonal Curves and Nonlinear Differential Equations

V. M. Buchstabera, D. V. Leikinb, V. Z. Ènol'skiib

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Institute of Magnetism, National Academy of Sciences of Ukraine

Abstract: We obtain an explicit realization of the Jacobi and Kummer varieties for trigonal curves of genus $g$ ($\gcd(g,3)=1$) of the form
$$ y^3=x^{g+1}+\sum_{\alpha,\beta}\lambda_{3\alpha +(g+1)\beta}x^{\alpha}y^{\beta},\qquad 0\le3\alpha+(g+1)\beta <3g+3, $$
as algebraic subvarieties in $\mathbb{C}^{4g+\delta}$, where $\delta=2(g-3[g/3])$, and in $\mathbb{C}^{g(g+1)/2}$. We uniformize these varieties with the help of $\wp$-functions of several variables defined on the universal space of Jacobians of such curves. By way of application, we obtain a system of nonlinear partial differential equations integrable in trigonal $\wp$-functions. This system in particular contains the oussinesq equation.


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English version:
Functional Analysis and Its Applications, 2000, 34:3, 159–171

Bibliographic databases:

UDC: 512.742+517.957
Received: 22.05.2000

Citation: V. M. Buchstaber, D. V. Leikin, V. Z. Ènol'skii, “Uniformization of Jacobi Varieties of Trigonal Curves and Nonlinear Differential Equations”, Funktsional. Anal. i Prilozhen., 34:3 (2000), 1–16; Funct. Anal. Appl., 34:3 (2000), 159–171

Citation in format AMSBIB
\by V.~M.~Buchstaber, D.~V.~Leikin, V.~Z.~\`Enol'skii
\paper Uniformization of Jacobi Varieties of Trigonal Curves and Nonlinear Differential Equations
\jour Funktsional. Anal. i Prilozhen.
\yr 2000
\vol 34
\issue 3
\pages 1--16
\jour Funct. Anal. Appl.
\yr 2000
\vol 34
\issue 3
\pages 159--171

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  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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