论文标题
$π$ -SMMETRIC SUPERGRASSMANIAN的自动形态和真实结构
Automorphisms and real structures for a $Π$-symmetric super-Grassmannian
论文作者
论文摘要
任何复杂的分析矢量束$ \ mathbb e $都承认自然定义的同性恋者$ ϕ_α $，$α\ in \ mathbb c^*$，即$ ϕ__α $是乘以本地部分的乘法，乘以复杂的数字$α$。我们调查了一个问题，何时可以将这些自动形态提升为对应于$ \ Mathbb E $的非分类超人。此外，我们计算了$π$ -smmetric超级格拉斯曼尼亚$π\！\！点。
Any complex-analytic vector bundle $\mathbb E$ admits naturally defined homotheties $ϕ_α$, $α\in \mathbb C^*$, i.e. $ϕ_α$ is the multiplication of a local section by a complex number $α$. We investigate the question when such automorphisms can be lifted to a non-split supermanifold corresponding to $\mathbb E$. Further, we compute the automorphism supergroup of a $Π$-symmetric super-Grassmannian $Π\!\operatorname{Gr}_{n,k}$, and, using Galois cohomology, we classify the real structures on $Π\!\operatorname{Gr}_{n,k}$ and compute the corresponding supermanifolds of real points.
