Given a smooth curve with weighted marked points, the Abel-Jacboi map produces a line bundle on the curve. This map fails to extend to the full boundary of the moduli space of stable pointed curves. Using ideas from logarithmic geometry, we describe a modular modification of the moduli space of curves over which the Abel-Jacobi map extends. This recovers the double ramification cycle as well as variants associated to differentials.

This work is joint with Jonathan Wise.