Uniformization of Jacobi varieties of trigonal curves and nonlinear differential equations

V. M. Buchstaber, V. Z. Enolskii, D. V. Leykin

Research output: Contribution to journalArticlepeer-review

42 Citations (Scopus)

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 y3 = x9+1 + ∑α,β λ3α+(g+1)βxαyβ, 0 ≤ 3α + (g + 1)β < 3g + 3, as algebraic subvarieties in ℂ4g+δ, where δ = 2(g - 3[g/3]), and in ℂg(g+1)/2. We uniformize these varieties with the help of ℘-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 ℘-functions. This system in particular contains the Boussinesq equation.

Original languageEnglish
Pages (from-to)159-171
Number of pages13
JournalFunctional Analysis and its Applications
Volume34
Issue number3
DOIs
Publication statusPublished - 2000
Externally publishedYes

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