Integrable linear equations and the Riemann-Schottky problem

Details Integrable linear equations and the Riemann-Schottky problem Integrable linear equations and the Riemann-Schottky problem

2005-04-10

arxiv.org/abs/math/0504192v2

Mathematics

Algebraic Geometry

20 pages, Latex, minor erros are corrected, missing argumants are clarified

Scientific paper

We prove that an indecomposable principally polarized abelian variety $X$ is
the Jacobain of a curve if and only if there exist vectors $U\neq 0,V$ such
that the roots $x_i(y)$ of the theta-functional equation $\theta(Ux+Vy+Z)=0$
satisfy the equations of motion of the {\it formal infinite-dimensional
Calogero-Moser system}

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