Stability conditions and moduli spaces for Kuznetsov components of Gushel–Mukai varieties
Stability conditions and moduli spaces for Kuznetsov components of Gushel–Mukai varieties
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DOI：
10.2140/gt.2022.26.3055
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发表时间：
2019-12
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影响因子：
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通讯作者：
Alexander Perry;L. Pertusi;Xiaolei Zhao
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文献类型：
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作者：
Alexander Perry;L. Pertusi;Xiaolei Zhao
我们证明了Gushel-Mukai变元的Kuznetsov分量上存在Bridgeland稳定条件，并在偶维情况下描述了这些范畴中Bridgeland半稳定对象的模空间结构。作为应用，我们构造了K3型极化超kahler变种的一元局部完备族的无穷级数，并在理论上刻画了偶数维Gushel-Mukai变种的Kuznetsov分量等价于K3曲面的派生范畴时的hodge -。
We prove the existence of Bridgeland stability conditions on the Kuznetsov components of Gushel-Mukai varieties, and describe the structure of moduli spaces of Bridgeland semistable objects in these categories in the even-dimensional case. As applications, we construct a new infinite series of unirational locally complete families of polarized hyperkahler varieties of K3 type, and characterize Hodge-theoretically when the Kuznetsov component of an even-dimensional Gushel-Mukai variety is equivalent to the derived category of a K3 surface.