论文标题
关于非必要正常仿射复曲面品种的自动形态学组
On the automorphism group of non-necessarily normal affine toric varieties
论文作者
论文摘要
我们的主要结果是以下内容：让X成为普通的仿生曲面表面，而没有圆圆度因子。然后存在一个非正常的仿射曲面表面X'，自动形构成X的自动形态X'，并且仅当X与仿射平面不同时，就存在X的自动形态。作为一种工具，我们首先在任何维度的非必要正常的仿射感谢您X上提供了标准化的添加剂组动作的分类。回想一下，X上的归一化添加剂动作与X的常规函数代数上的同质局部nilpotent推导相对应。我们更一般而言，我们在交换型单粒单杆的交换性收益型单杆的半元代数上提供了同质局部Nilpotent nilpotent衍生物的分类。
Our main result is the following: let X be a normal affine toric surface without torus factor. Then there exists a non-normal affine toric surface X' with automorphism group isomorphic to the automorphism group of X if and only if X is different from the affine plane. As a tool, we first provide a classification of normalized additive group actions on a non-necessarily normal affine toric variety X of any dimension. Recall that normalized additive group actions on X are in correspondence with homogeneous locally nilpotent derivations on the algebra of regular functions of X. More generally, we provide a classification of homogeneous locally nilpotent derivations on the semigroup algebra of a commutative cancellative monoid.
