Weierstrass Prym eigenforms in genus four

Erwan Lanneau; Duc-Manh Nguyen

doi:10.1017/s1474748019000057

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arXiv · 1802.04879

Weierstrass Prym eigenforms in genus four

Erwan Lanneau·Duc-Manh Nguyen

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Abstract

We prove that for each discriminant $D \equiv 0,1 \mod 4, D \not\in\{4,9\}$, the corresponding Prym eigenform locus discovered by McMullen in the stratum $\mathcal{H}(6)$ is connected. Thus, the projection of any of those loci in the moduli space is a single Teichm\"uller curve. Along the way, we obtain a classification of primitive square-tiled surfaces in the locus $\mathrm{Prym}(6)$ of Prym forms in $\mathcal{H}(6)$.

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BibTeX RIS

Erwan Lanneau, Duc-Manh Nguyen. 2018-02-13. Weierstrass Prym eigenforms in genus four. https://doi.org/10.1017/s1474748019000057

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