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Mathematics, Algebraic Geometry
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.