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      Automorphism groups of cubic fourfolds and K3 categories

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          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.

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          Most cited references14

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          Stability conditions on triangulated categories

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            On K3 surfaces with large Picard number

            D Morrison (1984)
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              Stability conditions on $K3$ surfaces

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                Author and article information

                Journal
                24 September 2019
                Article
                1909.11033
                0c7b2d26-fd4a-4d54-9399-297406c6c708

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Custom metadata
                RIKEN-iTHEMS-Report-19
                36 pages
                math.AG

                Geometry & Topology
                Geometry & Topology

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