Integrable linear equations and the Riemann-Schottky problem

  • I. Krichever
Part of the Progress in Mathematics book series (PM, volume 253)


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.


Wave Solution Meromorphic Function Abelian Variety Pseudodifferential Operator Spectral Curve 
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© Birkhäuser Boston 2006

Authors and Affiliations

  • I. Krichever
    • 1
    • 2
  1. 1.Department of MathematicsColumbia UniversityNew YorkUSA
  2. 2.Landau Institute for Theoretical PhysicsMoscowRussia

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