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arXiv · 1912.06935

Stability conditions and moduli spaces for Kuznetsov components of Gushel-Mukai varieties

Alexander Perry·Laura Pertusi·Xiaolei Zhao
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Abstract

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 hyperk\"{a}hler 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.

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Alexander Perry, Laura Pertusi, Xiaolei Zhao. 2019-12-14. Stability conditions and moduli spaces for Kuznetsov components of Gushel-Mukai varieties. https://doi.org/10.2140/gt.2022.26.3055

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