Geodesic
Smooth Compactifications of the Abel-Jacobi Section
Forum of Mathematics, Sigma, Tome 11 (2023)

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For $\theta $ a small generic universal stability condition of degree $0$ and A a vector of integers adding up to $-k(2g-2+n)$, the spaces $\overline {\mathcal {M}}_{g,A}^\theta $ constructed in [AP21, HMP+22] are observed to lie inside the space $\textbf {Div}$ of [MW20], and their pullback under $\textbf {Rub} \to \textbf {Div}$ of loc. cit. to be smooth. This provides smooth and modular modifications $\widetilde {\mathcal {M}}_{g,A}^\theta $ of $\overline {\mathcal {M}}_{g,n}$ on which the logarithmic double ramification cycle can be calculated by several methods. 
@article{10_1017_fms_2023_83,
     author = {Sam Molcho},
     title = {Smooth {Compactifications} of the {Abel-Jacobi} {Section}},
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Sam Molcho. Smooth Compactifications of the Abel-Jacobi Section. Forum of Mathematics, Sigma, Tome 11 (2023). doi: 10.1017/fms.2023.83

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