Geodesic
The closure of double ramification loci via strata of exact differentials
Documenta mathematica, Tome 27 (2022), pp. 2625-2656.

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Double ramification loci, also known as strata of $0$-differentials, are algebraic subvarieties of the moduli space of smooth curves parametrizing Riemann surfaces such that there exists a rational function with prescribed ramification over $0$ and $\infty$. We describe the closure of double ramification loci inside the Deligne-Mumford compactification in geometric terms. To a rational function we associate its exact differential, which allows us to realize double ramification loci as linear subvarieties of strata of meromorphic differentials. We then obtain a geometric description of the closure using our recent results on the boundary of linear subvarieties. Our approach yields a new way of relating the geometry of loci of rational functions and Teichmüller dynamics. We also compare our results to a different approach using admissible covers.
Classification : 14H15
Keywords: strata of differentials, moduli space of curves, double ramification cycles 
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     author = {Benirschke, Frederik},
     title = {The closure of double ramification loci via strata of exact differentials},
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     volume = {27},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a2/}
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Benirschke, Frederik. The closure of double ramification loci via strata of exact differentials. Documenta mathematica, Tome 27 (2022), pp. 2625-2656. http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a2/