The closure of double ramification loci via strata of exact differentials (Q2695715)

Summary: 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.