论文标题
在托拉尔品种的自动形态群体上
On the automorphism group of a toral variety
论文作者
论文摘要
令$ \ mathbb {k} $为特征零的代数封闭字段。如果它与torus $的封闭子变量同构（\ Mathbb {k}^*）^d $同构，则Affine代数品种$ x $ x $ x $ ymathbb {k} $是折磨。我们研究了toral品种的常规汽车$ x $的$ \ mathrm {aut}（x）$。我们证明，如果$ t $是$ \ mathrm {aut}（x）$中的最大圆环，则$ x $是直接的产品$ y \ times t $，其中$ y $是y的摩尔群品种，在自动形态群中具有微不足道的最大圆环。我们表明，知道$ \ mathrm {aut}（y）$，一个人可以计算$ \ mathrm {aut}（x）$。在组$ \ mathbb {k} [y]^*/\ mathbb {k}^*$ is $ \ dim y + 1 $的情况下，可以明确描述$ \ mathrm {aut}（y）$。
Let $\mathbb{K}$ be an algebraically closed field of characteristic zero. An affine algebraic variety $X$ over $\mathbb{K}$ is toral if it is isomorphic to a closed subvariety of a torus $(\mathbb{K}^*)^d$. We study the group $\mathrm{Aut}(X)$ of regular automorpshims of a toral variety $X$. We prove that if $T$ is a maximal torus in $\mathrm{Aut}(X)$, then $X$ is a direct product $Y\times T$, where $Y$ is a toral variety with a trivial maximal torus in the automorphism group. We show that knowing $\mathrm{Aut}(Y)$, one can compute $\mathrm{Aut}(X)$. In the case when the rank of the group $\mathbb{K}[Y]^*/\mathbb{K}^*$ is $\dim Y + 1$, the group $\mathrm{Aut}(Y)$ can be described explicitly.
