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

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