Automorphism groups of cubic fourfolds and K3 categories

TL;DR

This paper explores the connections between automorphism groups of cubic fourfolds, their Kuznetsov components, and associated K3 surfaces, revealing structural relationships and conditions for symplectic automorphisms.

Contribution

It characterizes automorphism groups of cubic fourfolds via Bridgeland stability, compares them with K3 surface automorphisms, and links symplectic automorphisms to associated K3 surfaces.

Findings

Automorphism groups of cubic fourfolds are subgroups of autoequivalence groups of Kuznetsov components.

Existence of non-trivial symplectic automorphisms relates to associated K3 surfaces.

Automorphism groups of cubic fourfolds can be characterized through stability conditions.

Abstract

In this paper, we study relations between automorphism groups of cubic fourfolds and Kuznetsov components. Firstly, we characterize automorphism groups of cubic fourfolds as subgroups of autoequivalence groups of Kuznetsov components using Bridgeland stability conditions. Secondly, we compare automorphism groups of cubic fourfolds with automorphism groups of their associated K3 surfaces. Thirdly, we note that the existence of a non-trivial symplectic automorphism on a cubic fourfold is related to the existence of associated K3 surfaces.