2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101193We 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 $θ(Ux+Vy+Z)=0$ satisfy the equations of motion of the {\it formal infinite-dimensional Calogero-Moser system}20 pages, Latex, minor erros are corrected, missing argumants are clarifiedAlgebraic GeometryHigh Energy Physics - TheoryMathematical Physicstext