We prove that an indecomposable principally polarized abelian variety X is the Jacobain of a curve if and only if there exist vectors U ≠ 0, V such that the roots xi(y) of the theta-functional equation θ(Ux + Vy + Z) = 0 satisfy the equations of motion of the formal infinite-dimensional Calogero–Moser system.
CITATION STYLE
Krichever, I. (2006). Integrable linear equations and the riemann–Schottky problem. In Progress in Mathematics (Vol. 253, pp. 497–514). Springer Basel. https://doi.org/10.1007/978-0-8176-4532-8_8
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