Logarithmic structures and the double ramification cycle on the moduli space of curves

Logarithmic structures and the double ramification cycle on the moduli space of curves

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Steffen Marcus, The College of New Jersey
Fine Hall 322

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.