Automorphisms of two-dimensional quadrics

TL;DR

This paper investigates the automorphism groups of smooth two-dimensional rational quadrics over fields of characteristic zero, focusing on the maximum Jordan constants achievable based on the fields' arithmetic properties.

Contribution

It determines the maximum Jordan constants for automorphism groups of such quadrics, linking these maxima to the arithmetic properties of the underlying fields.

Findings

Identified maximum Jordan constants for automorphism groups.

Connected field arithmetic properties to automorphism group behavior.

Provided bounds depending on field characteristics.

Abstract

In this paper, we find the maximum values that the Jordan constant of the automorphism group of a smooth two-dimensional rational quadric over a field of characteristic zero can attain, depending on the arithmetic properties of a field.