Connected components of strata of residueless meromorphic differentials (2310.07775v3)

Abstract: Generalized strata of meromorphic differentials are loci in the usual strata of differentials, where certain sets of residues sum up to zero. They appear naturally in the boundary of the multi-scale compactification of the usual strata. Enumerating the connected components of generalized strata is necessary to understand the boundary complex of the multi-scale compactification. In this paper we classify connected components of the strata of residueless meromorphic differentials, which are the strata with the maximum possible number of conditions imposed on the residues of the poles.