On Gizatullin's Problem for quartic surfaces of Picard rank $2$

TL;DR

This paper investigates which automorphisms of general smooth quartic surfaces with Picard rank 2 can be realized as restrictions of Cremona transformations of the ambient projective space.

Contribution

It characterizes automorphisms of certain quartic surfaces that originate from Cremona transformations, addressing Gizatullin's problem in this specific setting.

Findings

Identifies automorphisms of quartic surfaces that are restrictions of Cremona transformations.

Provides criteria for when automorphisms are induced by Cremona transformations.

Advances understanding of the automorphism groups of quartic surfaces with Picard rank 2.

Abstract

In this paper we determine which automorphisms of general smooth quartic surfaces $S\subset \mathbb{P}^3$ of Picard rank $2$ are restrictions of Cremona transformations of $\mathbb{P}^3$.