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We provide a complete classification of Teichm\"uller curves occurring inhyperelliptic components of the meromorphic strata of differentials. Using anon-existence criterion based on how Teichm\"uller curves intersect theboundary of the moduli space we derive a contradiction to the algebraicity ofany candidate outside of Hurwitz covers of strata with projective dimension oneand Hurwitz covers of zero residue loci in strata with projective dimensiontwo.

Teichm\"uller curves in hyperelliptic components of meromorphic strata