Teichm\"uller curves in hyperelliptic components of meromorphic strata

Author:

Martin Möller, Scott Mullane

Keyword:

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

journal:

date:

2023-05-04 16:00:00

Abstract

We provide a complete classification of Teichm\"uller curves occurring in hyperelliptic components of the meromorphic strata of differentials. Using a non-existence criterion based on how Teichm\"uller curves intersect the boundary of the moduli space we derive a contradiction to the algebraicity of any candidate outside of Hurwitz covers of strata with projective dimension one and Hurwitz covers of zero residue loci in strata with projective dimension two.

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