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 ${\mathcal{H}}_g^2(\mu )$ are uniruled when $\mu$ is a positive partition of $4g-4$ and either $3⩽g⩽5$ or $g=6$ and $l(\mu )⩾4$.

中文翻译：

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低属差异地层的最大角度和地层不规则度

我们证明了对于阿贝尔层的非超椭圆分量中的通用元素${\mathcal{H}}_G(\mu )$属$G$，基础曲线具有最大的边角性。我们将此结果扩展到二次层的情况，当分区$\mu$有正面条目。因此，我们推断所有非超椭圆分量${\mathcal{H}}_9(\mu )$不规则时$\mu$是 16 和所有非超椭圆分量的正分区${\mathcal{H}}_G^2(\mu )$不规则时$\mu$是一个正分区$4G-4$并且要么$3⩽G⩽5$或者$G=6$和$l(\mu )⩾4$.