The Nagata automorphism is shifted linearizable
| dc.creator | Maubach, Stefan | |
| dc.creator | Poloni, Pierre-Marie | |
| dc.date | 2008-04-30 | |
| dc.date.accessioned | 2026-07-07T09:36:05Z | |
| dc.date.available | 2026-07-07T09:36:05Z | |
| dc.description | A polynomial automorphism $F$ is called {\em shifted linearizable} if there exists a linear map $L$ such that $LF$ is linearizable. We prove that the Nagata automorphism $N:=(X-YΔ-ZΔ^2,Y+ZΔ, Z)$ where $Δ=XZ+Y^2$ is shifted linearizable. More precisely, defining $L_{(a,b,c)}$ as the diagonal linear map having $a,b,c$ on its diagonal, we prove that if $ac=b^2$, then $L_{(a,b,c)}N$ is linearizable if and only if $bc\not = 1$. We do this as part of a significantly larger theory: for example, any exponent of a homogeneous locally finite derivation is shifted linearizable. We pose the conjecture that the group generated by the linearizable automorphisms may generate the group of automorphisms, and explain why this is a natural question. | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/0804.4870 | |
| dc.identifier | http://arxiv.org/abs/0804.4870 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/160049 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Commutative Algebra | |
| dc.subject | Complex Variables | |
| dc.subject | 14R10, 14R20, 14L17, 32M17 | |
| dc.title | The Nagata automorphism is shifted linearizable | |
| dc.type | text |