The Kadomtsev -- Petviashvili equation and relations for the periods of holomorphic differentials on Riemann surfaces

S. P. Novikov's conjecture that the relations between theta functions that follow from the nonlinear Kadomcev-Petviasvili equation, well known in mathematical physics, characterize the Jacobian varieties of Riemann surfaces among all abelian varieties is proved in this paper, except for the possibility of superfluous components