Stability conditions and moduli spaces forKuznetsov components of Gushel–Mukai varieties

Abstract

We prove the existence of Bridgeland stability conditions on the Kuznetsov\ncomponents of Gushel-Mukai varieties, and describe the structure of moduli\nspaces of Bridgeland semistable objects in these categories in the\neven-dimensional case. As applications, we construct a new infinite series of\nunirational locally complete families of polarized hyperk\\"{a}hler varieties of\nK3 type, and characterize Hodge-theoretically when the Kuznetsov component of\nan even-dimensional Gushel-Mukai variety is equivalent to the derived category\nof a K3 surface.\n