论文标题
涵盖积极特征的完全交叉点的性质
Covering gonalities of complete intersections in positive characteristic
论文作者
论文摘要
我们定义了在任意领域的覆盖范围和可分离性的覆盖范围，从而推广了Bastianelli-de Poi-ein lazarsfeld-ullery对复杂品种的定义。我们表明，在任意字段上，$ \ mathbb {p}^n $中平滑的多智能$（d_1，\ ldots，d_k）$完整的交叉点具有可分离的覆盖率，至少$ d-n+1 $，其中$ d = d_1+\ cdots+cdots+d_k $。我们还表明，如此一般的品种具有至少$ \ frac {d-n+2} {2} $。
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 $\frac{d-N+2}{2}$.
