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Funktsional'nyi Analiz i ego Prilozheniya, 2008, Volume 42, Issue 4, Pages 24–36
DOI: https://doi.org/10.4213/faa2926
(Mi faa2926)
 

This article is cited in 33 scientific papers (total in 34 papers)

Solution of the Problem of Differentiation of Abelian Functions over Parameters for Families of $(n,s)$-Curves

V. M. Buchstabera, D. V. Leikinb

a Steklov Mathematical Institute, Russian Academy of Sciences
b Institute of Magnetism, National Academy of Sciences of Ukraine
References:
Abstract: We consider a wide class of models of plane algebraic curves, so-called $(n,s)$-curves. The case $(2,3)$ is the classical Weierstrass model of an elliptic curve. On the basis of the theory of multivariate sigma functions, for every pair of coprime $n$ and $s$ we obtain an effective description of the Lie algebra of derivations of the field of fiberwise Abelian functions defined on the total space of the bundle whose base is the parameter space of the family of nondegenerate $(n,s)$-curves and whose fibers are the Jacobi varieties of these curves. The essence of the method is demonstrated by the example of Weierstrass elliptic functions. Details are given for the case of a family of genus 2 curves.
Keywords: sigma function, differentiation with respect to parameters, universal bundle of Jacobi varieties, $(n,s)$-curve, vector field tangent to the discriminant of a singularity.
Received: 03.09.2008
English version:
Functional Analysis and Its Applications, 2008, Volume 42, Issue 4, Pages 268–278
DOI: https://doi.org/10.1007/s10688-008-0040-4
Bibliographic databases:
Document Type: Article
UDC: 517.958+515.178.2
Language: Russian
Citation: V. M. Buchstaber, D. V. Leikin, “Solution of the Problem of Differentiation of Abelian Functions over Parameters for Families of $(n,s)$-Curves”, Funktsional. Anal. i Prilozhen., 42:4 (2008), 24–36; Funct. Anal. Appl., 42:4 (2008), 268–278
Citation in format AMSBIB
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  • This publication is cited in the following 34 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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