3. Compare $\mathrm{DR}_g^\mathrm{adm}(A)$ with $\mathrm{DR}_g^\mathrm{rel}(A)$
General Proposal : Compare $\mathrm{DR}_g^{\mathrm{adm}}(A)$ with $\mathrm{DR}_g^{\mathrm{rel}}(A)$. The latter object has been defined geometrically in different, mostly equivalent ways: Using the Abel-Jacobi map by Holmes, Kass - Pagani, Marcus - Wise, and using relative stable maps by Guéré, Marcus - Wise.Sub-question: Is the degree $2d$ part of $\mathrm{DR}_g^d(A)$ supported on some specific stable graphs (no loops?). -Answer: No, one get contributions from many different graphs
Cite this as: AimPL: Double ramification cycles and integrable systems, available at http://aimpl.org/doubleramific.