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arXiv · 2008.02183

Maximal gonality on strata of differentials and uniruledness of strata in low genus

Andrei Bud
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Abstract

We prove that for a generic element in a nonhyperelliptic component of an abelian stratum $\mathcal{H}_g(\mu)$ in genus $g$, the underlying curve has maximal gonality. We extend this result to the case of quadratic strata when the partition $\mu$ has positive entries. As a consequence we deduce that all nonhyperelliptic components of $\mathcal{H}_9(\mu)$ are uniruled when $\mu$ is a positive partition of 16 and all nonhyperelliptic components of $\mathcal{H}^2_g(\mu)$ are uniruled when $\mu$ is a positive partition of $4g-4$ and either $3\leq g\leq5$ or $g=6$ and $l(\mu)\geq 4$.

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Andrei Bud. 2020-08-05. Maximal gonality on strata of differentials and uniruledness of strata in low genus. https://doi.org/10.1112/blms.12515

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