The tame and the wild automorphisms of an affine quadric threefold

TL;DR

This paper demonstrates the existence of wild automorphisms on an affine quadric threefold, extending the understanding of automorphism complexity in algebraic geometry.

Contribution

It adapts methods from affine space automorphisms to establish wild automorphisms in the context of affine quadric threefolds.

Findings

Existence of wild automorphisms on affine quadric threefolds

Method adaptation from affine space automorphisms

Advancement in automorphism classification

Abstract

We prove the existence of wild automorphisms on an affine quadric threefold. The method we use is an adaptation of the one used by Shestakov and Umirbaev to prove the existence of wild automorphisms on the affine three dimensional space.