论文标题
具有全球向量场的弱del pezzo表面
Weak del Pezzo surfaces with global vector fields
论文作者
论文摘要
我们将平滑的弱del pezzo表面与全球向量字段进行分类，这是任意封闭的任意特征$ k $ $ p \ geq 0 $的$ k $。我们对这些表面上的$（1）$ - 和$（2）$的配置进行完整说明，并计算其自动形态方案的身份组成部分。事实证明，如果$ p \ neq 2,3 $，有$ 53 $不同的家族，而如果$ p = 3 $，则有61美元的此类家庭，如果$ p = 2 $，则有$ 61 $。这些家庭中的每一个最多都有一个模量。作为我们分类的副产品，遵循的是，当$ k $以外的情况下，弱的del pezzo表面存在于$ k $，并且仅当$ p \ in \ in \ {2,3 \} $中。
We classify smooth weak del Pezzo surfaces with global vector fields over an arbitrary algebraically closed field $k$ of arbitrary characteristic $p \geq 0$. We give a complete description of the configuration of $(-1)$- and $(-2)$-curves on these surfaces and calculate the identity component of their automorphism schemes. It turns out that there are $53$ distinct families of such surfaces if $p \neq 2,3$, while there are $61$ such families if $p = 3$, and $75$ such families if $p = 2$. Each of these families has at most one moduli. As a byproduct of our classification, it follows that weak del Pezzo surfaces with non-reduced automorphism scheme exist over $k$ if and only if $p \in \{2,3\}$.
