Integrable linear equations and the Riemann-Schottky problem

I. Krichever

Integrable linear equations and the Riemann-Schottky problem

Algebraic Geometry 2007-05-23 v2 High Energy Physics - Theory Mathematical Physics math.MP

Authors: I. Krichever

Abstract

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}

Keywords

jacobian conjecture

Cite

@article{arxiv.math/0504192,
  title  = {Integrable linear equations and the Riemann-Schottky problem},
  author = {I. Krichever},
  journal= {arXiv preprint arXiv:math/0504192},
  year   = {2007}
}

Comments

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

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