Smoothness of open double ramification loci in higher genus

Establish smoothness of the open double ramification locus in higher genus, potentially by constructing a normal-crossings compactification adapted from the theory of well-spaced maps.

Background

The paper discusses compactifications of higher-rank double ramification loci and notes that the space of rubber maps generally contains spurious components and is not a normal-crossings compactification. The authors indicate that, in genus one, a normal-crossings compactification should be obtainable by adapting the theory of well-spaced maps.

Such a compactification would imply smoothness of the open double ramification locus, a property that remains unknown in higher genus. The unresolved issue is therefore the smoothness itself, together with the geometric construction that would establish it.