论文标题
光滑仿射曲线上矢量场的Lie代数的支架宽度
Bracket width of the Lie algebra of vector fields on a smooth affine curve
论文作者
论文摘要
我们证明，矢量字段的简单谎言代数的支架宽度$ \ rm {vec}（c）$ a Place不可减至的仿射曲线$ c $，最多三个。此外，如果$ c $是平面曲线，则最多是$ \ rm {vec}（c）$的支架宽度最多是两个，如果此外$ c $在infinity中具有独特的位置，则$ \ rm {vec}（vec}（c）$的支架宽度正好是两个。 我们还表明，如果$ c $是理性的，则$ \ rm {vec}（c）$等于一个。
We prove that the bracket width of the simple Lie algebra of vector fields $\rm{Vec}(C)$ of a smooth irreducible affine curve $C$ with a trivial tangent sheaf is at most three. In addition, if $C$ is a plane curve, the bracket width of $\rm{Vec}(C)$ is at most two and if moreover $C$ has a unique place at infinity, the bracket width of $\rm{Vec}(C)$ is exactly two. We also show that in case $C$ is rational, the width of $\rm{Vec}(C)$ equals one.
