One-dimensional strata of residueless meromorphic differentials

Author:

Myeongjae Lee, Guillaume Tahar

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Dynamical Systems (math.DS), Geometric Topology (math.GT)

journal:

date:

2023-10-18 16:00:00

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.

PDF: One-dimensional strata of residueless meromorphic differentials.pdf