Smooth Compactifications of the Abel-Jacobi Section

Abstract

For $\theta$ a small generic universal stability condition of degree $0$ and $A$ a vector of integers adding up to $k(2g-2)$, the spaces ${\overline{M}}_{g,n}^{\theta }$ resolving the Abel-Jacobi section to the compactified Jacobian Pic^θconstructed in the work of Abreu-Pacini and Holmes-Molcho-Pandharipande-Pixton-Schmitt are observed to lie inside the space $\text{Div}$ of Marcus and Wise, and their pullback to the rubber space of loc. cit to be smooth. This provides smooth and modular blowups ${\tilde{M}}_{g,n}^{\theta }$ of the moduli space of stable curves on which the logarithmic double ramification cycle can be calculated by several methods, old and novel.

arXiv comment30 pages. Comments and suggestions welcome. v2: Fixed a broken reference, some minor rewording in the introduction