Logarithmic compactification of the Abel-Jacobi section

Abstract

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 logarithmic and tropical geometry, we describe a modular modification of the moduli space of curves over which the Abel-Jacobi map extends. We also describe the attendant deformation theory and virtual fundamental class of this moduli space. This recovers the double ramification cycle, as well as variants associated to differentials.

This paper supersedes arXiv:1310.5981 by the same authors. Logarithmic and tropical perspectives are employed, obtaining stronger results. 36 pages, 3 figures. v2 appears in the Proceedings of the London Mathematical Society

References in corpus (4)

• A moduli stack of tropical curves
• Moduli of stable maps in genus one and logarithmic geometry I
• Extending the double ramification cycle by resolving the Abel-Jacobi map
• On log motives

Cited by in corpus (5)

• Infinitesimal structure of the pluricanonical double ramification locus
• A smooth compactification of the space of genus two curves in projective space via logarithmic geometry and Gorenstein curves
• Curve counting in genus one: elliptic singularities & relative geometry
• Rubber tori in the boundary of expanded stable maps
• Hyperelliptic Gorenstein curves and logarithmic differentials