We define the covering gonality and separable covering gonality of varieties over arbitrary fields, generalizing the definition given by Bastianelli, De Poi, Ein, Lazarsfeld, and Ullery for complex varieties. We show that, over an algebraically closed field, a smooth multidegree $(d_1,\dots <!--FUNCTION\; APPLICATION-->,d_k)$ 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 hypersurface has covering gonality at least $\frac{1}{2}(d-N+2)$.

中文翻译：

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以正面特征覆盖完整交叉口的边角

我们定义了任意域上品种的覆盖角和可分离覆盖角，概括了 Bastianelli、De Poi、Ein、Lazarsfeld 和 Ullery 对复杂品种给出的定义。我们证明，在代数闭域上，平滑的多度$(d_1,\dots <!--FUNCTION\; APPLICATION-->,d_{ķ})$完整的交叉点${\mathbb{P}}^{ñ}$至少具有可分离的覆盖角$d-ñ+1$， 在哪里$d=d_1+\cdots +d_{ķ}$. 我们还表明，非常普遍的这种超曲面至少具有覆盖边角性$\frac{1}{2}(d-ñ+2)$.