Characterization of affine $\mathbb{G}_m$-surfaces of hyperbolic type
| Autor: | Regeta, Andriy |
|---|---|
| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 8 pages; comments are welcome |
| Databáze: | arXiv |
| Externí odkaz: |
|