One-dimensional strata of residueless meromorphic differentials
Abstract
In projectivized strata of meromorphic 1-forms on elliptic curves with only one zero, the locus of residueless differentials is a complex curve endowed with a canonical complex projective structure. Drawing on the multi-scale compactification of strata, we provide formulas to compute the genus of these curves and the degree of their natural forgetful map to M1,1. Additionally, we distinguish two non-hyperelliptic components in the residueless locus of the exceptional stratum H1(12,-3,-3,-3,-3) and hence complete the classification of the connected components of these loci.
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