Hassett-Tschinkel correspondence and automorphisms of the quadric

TL;DR

This paper investigates the unique locally transitive actions of a commutative unipotent group on nondegenerate quadrics in projective space, establishing their classification up to isomorphism.

Contribution

It proves the uniqueness of such group actions on quadrics for each dimension, enriching the understanding of automorphism groups of quadrics.

Findings

Each nondegenerate quadric admits a unique locally transitive unipotent group action.

The classification of these actions is complete up to isomorphism.

The results connect to the Hassett-Tschinkel correspondence in automorphism group studies.

Abstract

We study locally transitive actions of the commutative unipotent group $\Gan$ on a nondegenerate quadric in the projective space $\P^{n+1}$. It is shown that for each $n$ such an action is unique up to isomorphism.