正特征完全交的覆盖角
Covering gonalities of complete intersections in positive characteristic
摘要：
本文定义了任意域上簇的覆盖性和可分覆盖性，推广了Bastianelli-de Poi-Ein-Lazarsough-Ullery关于复簇的定义.本文证明了在任意域上，$\mathbb{P}^N$中的光滑多度$(d_1,\ldots,d_k)$完全交至少具有可分覆盖角性$d-N+1$，其中$d=d_1+\cdots+d_k$ .我们还证明了非常一般的簇至少具有覆盖性$\frac{d-N+2}{2}$。
英文摘要：
We define the covering gonality and separable covering gonality of varieties over arbitrary fields, generalizing the definition given by Bastianelli-de Poi-Ein-Lazarsfeld-Ullery for complex varieties. We show that over an arbitrary field a smooth multidegree $(d_1,\ldots,d_k)$ complete intersection in $\mathbb{P}^N$ has separable covering gonality at least $d-N+1$, where $d=d_1+\cdots+d_k$. We also show that the very general such variety has covering gonality at least $\frac{d-N+2}{2}$.
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