论文标题
仿射Veronese表面的自动形态
Automorphisms of affine Veronese surfaces
论文作者
论文摘要
我们证明，subergebra $ k [x^n，x^n，x^n，x^{n-1} y，\ ldots，xy^{n-1}，y^n] $的每个派生和每个本地nilpotent衍生和本地nilpotent推导$ k [x，y] $。此外，我们证明，$ k [x^n，x^{n-1} y，\ ldots，xy^{n-1}，y^n] $的每一个自动形态零是$ k [x，y] $。我们还表明，$ k [x^n，x^{n-1} y，\ ldots，xy^{n-1}的一组自动形态学，y^n] $允许合并的免费产品结构。
We prove that every derivation and every locally nilpotent derivation of the subalgebra $K[x^n, x^{n-1}y,\ldots,xy^{n-1}, y^n]$, where $n\geq 2$, of the polynomial algebra $K[x,y]$ in two variables over a field $K$ of characteristic zero is induced by a derivation and a locally nilpotent derivation of $K[x,y]$, respectively. Moreover, we prove that every automorphism of $K[x^n, x^{n-1}y,\ldots,xy^{n-1}, y^n]$ over an algebraically closed field $K$ of characteristic zero is induced by an automorphism of $K[x,y]$. We also show that the group of automorphisms of $K[x^n, x^{n-1}y,\ldots,xy^{n-1}, y^n]$ admits an amalgamated free product structure.
