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7. The Tropical DR cycle

Proposed by Andreas Gross:

There exist tropical DR loci \mathrm{DR}_g^{\mathrm{trop}}(A) (Ulirsch, Zakharov) in the tropical moduli spaces \mathcal M_{g,n}^{\mathrm{trop}} of curves. They are the tropicalizations of the cycles \mathrm{DR}^{\mathrm{adm}}_g(A).
  1. Add multiplicities to the top-dimensional cones of \mathrm{DR}_g^{\mathrm{trop}}(A) to make it a tropical cycle.
  2. Compare the resulting cycle with the JPPZ formula. Start in genus g=1, where one has to compare codimension-1 classes.
  3. Further develop tropical intersection theory to make it work in higher genus.

      Cite this as: AimPL: Double ramification cycles and integrable systems, available at http://aimpl.org/doubleramific.