Summary
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 x i(y) of the theta-functional equation θ(Ux + Vy + Z) = 0 satisfy the equations of motion of the formal infinite-dimensional Calogero-Moser system.
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Krichever, I. (2006). Integrable linear equations and the Riemann-Schottky problem. In: Ginzburg, V. (eds) Algebraic Geometry and Number Theory. Progress in Mathematics, vol 253. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4532-8_8
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DOI: https://doi.org/10.1007/978-0-8176-4532-8_8
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