Solution of the problem of differentiation of abelian functions over parameters for families of \((n, s)\)-curves

DOI10.1007/s10688-008-0040-4zbMath1156.14315OpenAlexW2007047441MaRDI QIDQ1002831

Victor M. Buchstaber, Dmitry Leykin

Publication date: 26 February 2009

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10688-008-0040-4

zbMATH Keywords

sigma functiondifferentiation with respect to parametersuniversal bundle of Jacobi varieties

Mathematics Subject Classification ID

Plane and space curves (14H50) Analytic theory of abelian varieties; abelian integrals and differentials (14K20) Theta functions and curves; Schottky problem (14H42)

Related Items (20)

Degeneration of trigonal curves and solutions of the KP-hierarchy ⋮ On regularization of second kind integrals ⋮ ON DEGENERATE SIGMA-FUNCTIONS IN GENUS 2 ⋮ Periods of second kind differentials of $(n,s)$-curves ⋮ Geometric differential equations on bundles of Jacobians of curves of genus 1 and 2 ⋮ Hyperelliptic sigma functions and Adler-Moser polynomials ⋮ Solution of the Jacobi inversion problem on non-hyperelliptic curves ⋮ The field of meromorphic functions on a sigma divisor of a hyperelliptic curve of genus 3 and applications ⋮ Explicit formulas for differentiation of hyperelliptic functions ⋮ Lie algebras of heat operators in a nonholonomic frame ⋮ A uniqueness theorem for the two-dimensional sigma function ⋮ Parametric Korteweg-de Vries hierarchy and hyperelliptic sigma functions ⋮ Аналитические и теоретико-числовые свойства двумерных сигма-функций ⋮ Differentiation of genus 3 hyperelliptic functions ⋮ Polynomial dynamical systems and the Korteweg-de Vries equation ⋮ Equivariant functions and integrals of elliptic functions ⋮ Sigma functions and Lie algebras of Schrödinger operators ⋮ On the problem of differentiation of hyperelliptic functions ⋮ The sigma function over a family of curves with a singular fiber ⋮ Viktor Matveevich Buchstaber (on his 70th birthday)

Cites Work

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• Factorization of a weakly hyperbolic bundle
• The index of a vector field tangent to an odd-dimensional hypersurface and the signature of the relative Hessian

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