论文标题
仿射的特征$ \ mathbb {g} _m $ - 双曲线类型
Characterization of affine $\mathbb{G}_m$-surfaces of hyperbolic type
论文作者
论文摘要
在此注释中，我们证明，如果$ s $是一种非态$ \ mathbb {g} _m $ - ym $ -surface of yromy-surface of yromybolic类型，则承认$ \ mathbb {g} _a $ -action _a $ - action and $ x $是一个仿真的不可记述的品种$ \ mathbb {g} _m $ - 双曲线类型的表面。此外，我们表明，光滑的Danielewski表面$ dp = \ {xy = p（z）\} \ subset \ subset \ mathbb {a}^3 $，其中$ p $没有多个根，由其自动形态群体确定，被视为亲和性不可降低品种类别中的类别。
In this note we prove that if $S$ is an affine non-toric $\mathbb{G}_m$-surface of hyperbolic type that admits a $\mathbb{G}_a$-action and $X$ is an affine irreducible variety such that $Aut(X)$ is isomorphic to $Aut(S)$ as an abstract group, then $X$ is a $\mathbb{G}_m$-surface of hyperbolic type. Further, we show that a smooth Danielewski surface $Dp = \{ xy = p(z) \} \subset \mathbb{A}^3$, where $p$ has no multiple roots, is determined by its automorphism group seen as an ind-group in the category of affine irreducible varieties.
