论文标题
低属地层的差分和层次层面的地层的最大性质
Maximal gonality on strata of differentials and uniruledness of strata in low genus
论文作者
论文摘要
我们证明，对于Abelian Stratum $ \ MATHCAL {H} _G（μ）$ g $ $ g $的非遗传元素中的通用元素，基础曲线具有最大的性质。当分区$μ$具有正条目时，我们将此结果扩展到二次地层的情况。结果，我们推断出，当$μ$ $μ$是16的阳性分区时，所有非遗传性成分均为$ \ MATHCAL {h} _9（μ）$，而所有非遗传组件的$ \ Mathcal {h}^2_g（μ）$ $ $ $是$ $ $ $ $ $ 4，则所有非遗传组件是$ $ $ $ $ $ 4 g \ leq5 $或$ g = 6 $和$ l（μ）\ geq 4 $。
We prove that for a generic element in a nonhyperelliptic component of an abelian stratum $\mathcal{H}_g(μ)$ in genus $g$, the underlying curve has maximal gonality. We extend this result to the case of quadratic strata when the partition $μ$ has positive entries. As a consequence we deduce that all nonhyperelliptic components of $\mathcal{H}_9(μ)$ are uniruled when $μ$ is a positive partition of 16 and all nonhyperelliptic components of $\mathcal{H}^2_g(μ)$ are uniruled when $μ$ is a positive partition of $4g-4$ and either $3\leq g\leq5$ or $g=6$ and $l(μ)\geq 4$.
