论文标题
RDP del pezzo表面具有奇数特征的全局向量字段
RDP del Pezzo surfaces with global vector fields in odd characteristic
论文作者
论文摘要
我们将RDP del Pezzo表面与全球向量字段进行分类，这是特征性$ p \ neq 2 $的任意代数封闭字段。在特征$ 0 $中，每个rdp del pezzo表面$ x $都是等价的，也就是说，$ {\ rm aut} _x = {\ rm aut} _ {\ widetilde {x}} $，$ \ widetilde {x} $是全球范围的$ x $ x $ x $ x $ x $ x $ x $ x $ x $ x $相当于与全球向量场的弱del pezzo表面的分类。 在本文中，我们表明，如果$ p \ neq 2,3,5,7 $，那么每个RDP del pezzo表面都是均等的。我们在特征$ p = 3,5,7 $中对非等级的RDP del pezzo表面进行了分类，并在所有可能的程度上为每个此类RDP Del Pezzo表面提供明确的方程式。作为一个应用程序，我们在不完美的特征$ 7 $的字段上构造了常规的非平滑RDP Del Pezzo表面，从而表明该特征的已知绑定$ P \ leq 7 $在这种表面可以存在的特征上很敏锐。
We classify RDP del Pezzo surfaces with global vector fields over arbitrary algebraically closed fields of characteristic $p \neq 2$. In characteristic $0$, every RDP del Pezzo surface $X$ is equivariant, that is, ${\rm Aut}_X = {\rm Aut}_{\widetilde{X}}$, where $\widetilde{X}$ is the minimal resolution of $X$, hence the classification of RDP del Pezzo surfaces with global vector fields is equivalent to the classification of weak del Pezzo surfaces with global vector fields. In this article, we show that if $p \neq 2,3,5,7$, then it is still true that every RDP del Pezzo surface is equivariant. We classify the non-equivariant RDP del Pezzo surfaces in characteristic $p = 3,5,7$, giving explicit equations for every such RDP del Pezzo surface in all possible degrees. As an application, we construct regular non-smooth RDP del Pezzo surfaces over imperfect fields of characteristic $7$, thereby showing that the known bound $p \leq 7$ for the characteristics, where such a surface can exist, is sharp.
