论文标题
刚性仿射表面的自动形态组：身份分量
Automorphism groups of rigid affine surfaces: the identity component
论文作者
论文摘要
众所周知，投影代数变体的自动形态组的身份成分是代数组。对于准标记品种而言，这通常不是事实。在本说明中，我们解决了一个问题：给定一个自动形态组$ {\ rm aut}（y aut}（y）$的身份组件$ {\ rm aut}^0（y）$的身份组件$ {\ rm aut}^0（y）$是一个代数组？我们表明，这种情况只有$ y $不承认该添加剂组的有效行动，才会发生这种情况。在后一种情况下，$ {\ rm aut}^0（y）$是等级$ \ le 2 $的代数。
It is known that the identity component of the automorphism group of a projective algebraic variety is an algebraic group. This is not true in general for quasi-projective varieties. In this note we address the question: given an affine algebraic surface $Y$, as to when the identity component ${\rm Aut}^0 (Y)$ of the automorphism group ${\rm Aut} (Y)$ is an algebraic group? We show that this happens if and only if $Y$ admits no effective action of the additive group of the field. In the latter case, ${\rm Aut}^0 (Y)$ is an algebraic torus of rank $\le 2$.
