Generalized strata of meromorphic differentials with residue conditions are classified by hyperellipticity, ramification profile, spin parity, rotation number, and index.
One-dimensional strata of residueless meromorphic differentials
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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 $\mathcal{M}_{1,1}$. Additionally, we distinguish two non-hyperelliptic components in the residueless locus of the exceptional stratum $\mathcal{H}_{1}(12,-3,-3,-3,-3)$ and hence complete the classification of the connected components of these loci.
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math.AG 1years
2025 1verdicts
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Connected components of generalized strata of meromorphic differentials with residue conditions
Generalized strata of meromorphic differentials with residue conditions are classified by hyperellipticity, ramification profile, spin parity, rotation number, and index.