Connected components of generalized strata of meromorphic differentials with residue conditions

2025/04/28 by Lee, Myeongjae, Wong, Yiu Man · 1 citation
#Algebraic Geometry (math.AG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2504.20165

Abstract

Generalized strata of meromorphic differentials are loci within the usual strata of differentials where certain sets of residues sum to zero. They naturally appear in the boundary of the multi-scale compactification of the usual strata. The classification of generalized strata is a key step towards understanding the irreducible components of the boundary strata of the multi-scale compactification. The connected components of generalized strata of residueless differentials were classified in \citelee2023connected. In the present paper, we classify the connected components of generalized strata of meromorphic differentials in full generality.

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• Isoresidual fibrations and the birational geometry of moduli of pointed stable curves

Related

• Connected components of strata of residueless meromorphic differentials
• Connectedness of the boundaries of the strata of differentials
• Ends of the strata of differentials
• One-dimensional strata of residueless meromorphic differentials
• Connected components of the strata of the moduli space of meromorphic differentials