FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1998, VOLUME 4, NUMBER 1, PAGES 367-460

E. E. Demidov

Abstract

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The article is based on a special course delivered by the author in
the Independent Moscow university. It contains a detailed explanation
of several interrelations between soliton equations, infinite
dimensional Grassmann manifold and jacobians of the algebraic curves.
All these permit one to prove the (weakened) version of S. P. Novikov's
conjecture (based on I. M. Krichever's results) on characterization of
jacobians among all abelian tori by cheking whether the (corrected)
theta-function of the given abelian variety is a solution of the
Kadomtsev--Petviashvili non-linear differential equation.
```

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Last modified: April 8, 1998