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2 results

  • Tropical moments of tropical Jacobians

  • Part of
  • Robin de Jong, Farbod Shokrieh
  • Journal:
    Canadian Journal of Mathematics / Volume 75 / Issue 4 / August 2023
    Published online by Cambridge University Press:
    24 May 2022, pp. 1045-1075
    Print publication:
    August 2023
    • Article
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  • Each metric graph has canonically associated to it a polarized real torus called its tropical Jacobian. A fundamental real-valued invariant associated to each polarized real torus is its tropical moment. We give an explicit and efficiently computable formula for the tropical moment of a tropical Jacobian in terms of potential theory on the underlying metric graph. We show that there exists a universal linear relation between the tropical moment, a certain capacity called the tau invariant, and the total length of a metric graph. To put our formula in a broader context, we relate our work to the computation of heights attached to principally polarized abelian varieties.