论文标题
特征三的曲线曲线的ekedahl-oort阶层
Ekedahl-Oort strata of curves of genus four in characteristic three
论文作者
论文摘要
我们研究了Moduli空间上的诱导的Ekedahl-oort分层$ \ MATHCAL {M} _4 curves of属属的特征$ 3 $。通过构建具有给定ekedahl-oort类型的曲线家族，并通过计算诱导的ekedahl-oort地层与边界分裂类别的相交的维度，我们表明，对于某些诱导的ekedahl-oort阶层，$ \ \ \ \ \ \ \ \ \级{m} _4 $中的$ \ mathsensive in $ \ \ \ \ \ \ \ \米{M， Moduli空间中的Ekedahl-oort阶层$ \ MATHCAL {A} _4 $的主要极化Abelian dimension $ 4 $。
We study the induced Ekedahl-Oort stratification on the moduli space $\mathcal{M}_4$ of curves of genus $4$ in characteristic $3$. By constructing families of curves with given Ekedahl-Oort type and by computing the dimension of the intersection of the induced Ekedahl-Oort strata and the boundary divisor classes, we show that for certain induced Ekedahl-Oort strata in $\mathcal{M}_4$, they have the same codimension in $\mathcal{M}_4$ as the corresponding Ekedahl-Oort strata in moduli space $\mathcal{A}_4$ of principally polarized abelian varieties of dimension $4$.
