论文标题
广义费马特歧管的自其形态
Automorphisms of Generalized Fermat manifolds
论文作者
论文摘要
令$ d \ geq 1 $，$ k \ geq 2 $和$ n \ geq d+1 $是整数。 a $ d $维光滑复杂的代数$ m $称为$ $ $（d; k，n）$的广义费用，如果有一个Galois Holomorphic分支覆盖$π：m \ to {\ MathBb p}除数包括$ n+1 $ $的超级平面，每个平面都有$ k $的分支机构。在这种情况下，$ h $称为$ $（d; k，n）$的普通费玛特集团。在以前的工作中，我们证明了概括的Fermat Group $ H $在以下情况下是唯一的：（i）$ d = 1 $和$（k-1）（n-1）> 2 $，或（ii）$ d \ geq 2 $和$（d; k，n）\ notin \ notin \ {（2; 2; 2; 2; 2; 2; 2; 4,3; 4,3; 4,3; 4,3）$。为了获得这个独特的事实，我们使用了由于Kontogeorgis而使用的差异方法。本文提供了$ h $的独特性的不同，更短的证明。我们还研究了$ h $的子组的固定点的基因座。
Let $d \geq 1$, $k \geq 2$ and $n\geq d+1$ be integers. A $d$-dimensional smooth complex algebraic variety $M$ is called a generalized Fermat variety of type $(d;k,n)$ if there is a Galois holomorphic branched covering $π:M \to {\mathbb P}^{d}$, with deck group $H\cong {\mathbb Z}_{k}^{n}$, whose branch divisor consists of $n+1$ hyperplanes in general position, each one of branch order $k$. In this case, $H$ is called a generalized Fermat group of type $(d;k,n)$. In previous work, we proved that the generalized Fermat group $H$ is unique in the following cases: (i) $d=1$ and $(k-1)(n-1)>2$, or (ii) $d \geq 2$ and $(d;k,n) \notin \{(2;2,5), (2;4,3)\}$. To obtain this uniqueness fact, we used a differential method due to Kontogeorgis. This paper provides a different and shorter proof of the uniqueness of $H$. We also study the locus of fixed points of subgroups of $H$.
