三次四重和K3范畴的自同构群

IF 1.2 1区数学 Q1 MATHEMATICS

Algebraic Geometry Pub Date : 2019-09-24 DOI:10.14231/ag-2021-003

Genki Ouchi

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引用次数: 7

摘要

本文研究了三次四重的自同构群与库兹涅佐夫分量之间的关系。首先，我们利用Bridgeland稳定性条件将三次四重的自同构群刻画为库兹涅佐夫分量的自等价群的子群。其次，我们比较了三次四重的自同构群及其相关的K3曲面的自同构组。第三，我们注意到三次四重上非平凡辛自同构的存在性与相关的K3曲面的存在性有关。

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Automorphism groups of cubic fourfolds and K3 categories

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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来源期刊

Algebraic Geometry Mathematics-Geometry and Topology

CiteScore

2.40

自引率

0.00%

发文量

审稿时长

52 weeks

期刊介绍： This journal is an open access journal owned by the Foundation Compositio Mathematica. The purpose of the journal is to publish first-class research papers in algebraic geometry and related fields. All contributions are required to meet high standards of quality and originality and are carefully screened by experts in the field.