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Uspekhi Mat. Nauk, 2008, Volume 63, Issue 6(384), Pages 19–30 (Mi umn9243)  

This article is cited in 1 scientific paper (total in 1 paper)

Abelian solutions of the soliton equations and Riemann–Schottky problems

I. M. Kricheverab

a L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
b Columbia University

Abstract: The present article is an exposition of the author's talk at the conference dedicated to the 70th birthday of S. P. Novikov. The talk contained the proof of Welters' conjecture which proposes a solution of the classical Riemann–Schottky problem of characterizing the Jacobians of smooth algebraic curves in terms of the existence of a trisecant of the associated Kummer variety, and a solution of another classical problem of algebraic geometry, that of characterizing the Prym varieties of unramified covers.

DOI: https://doi.org/10.4213/rm9243

Full text: PDF file (539 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2008, 63:6, 1011–1022

Bibliographic databases:

UDC: 517.9
MSC: 14H40, 14H42, 37K10
Received: 02.09.2008

Citation: I. M. Krichever, “Abelian solutions of the soliton equations and Riemann–Schottky problems”, Uspekhi Mat. Nauk, 63:6(384) (2008), 19–30; Russian Math. Surveys, 63:6 (2008), 1011–1022

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. Ma W.-X., “Trigonal Curves and Algebro-Geometric Solutions to Soliton Hierarchies i”, Proc. R. Soc. A-Math. Phys. Eng. Sci., 473:2203 (2017), 20170232  crossref  mathscinet  isi  scopus
  • Успехи математических наук Russian Mathematical Surveys
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