论文标题
关于克莱因高空曲面自动形态的托雷利原理
On a Torelli Principle for automorphisms of Klein hypersurfaces
论文作者
论文摘要
利用Oguiso和Yu引入的差分方法的完善，我们提供了有效的条件，在该条件下，$ \ Mathbf {p}^{n+1}的平滑度$ D $ hypersurface的自动形态由广义三角矩阵提供。应用此标准，我们计算了dimension $ n \ geq 1 $和$ d \ geq 3 $的所有剩余的klein hypersurfaces的剩余自动形态群，其中$（n，d）\ neq（2,4）$。我们介绍了极端两极分化的Hodge结构的概念，该结构是允许大质量的自动形态的结构。使用这个概念，我们计算了我们称为Wagstaff类型的某些Klein Hypersurfaces的极化Hodge结构的自动形态群，其特征在于存在大型质量序列的自动形态。对于Cutic Hypersurfaces和其他一些$（N，D）$的值，我们表明这两个组正如Torelli原则所预测的那样（达到互动）。
Using a refinement of the differential method introduced by Oguiso and Yu, we provide effective conditions under which the automorphisms of a smooth degree $d$ hypersurface of $\mathbf{P}^{n+1}$ are given by generalized triangular matrices. Applying this criterion we compute all the remaining automorphism groups of Klein hypersurfaces of dimension $n\geq 1$ and degree $d\geq 3$ with $(n,d)\neq (2,4)$. We introduce the concept of extremal polarized Hodge structures, which are structures that admit an automorphism of large prime order. Using this notion, we compute the automorphism group of the polarized Hodge structure of certain Klein hypersurfaces that we call of Wagstaff type, which are characterized by the existence of an automorphism of large prime order. For cubic hypersurfaces and some other values of $(n,d)$, we show that both groups coincide (up to involution) as predicted by the Torelli Principle.
