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

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 hyperkähler 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.

47 pages, minor updates, final version

References in corpus (2)

• Mapping class group and global Torelli theorem for hyperkahler manifolds: an erratum
• Categorical cones and quadratic homological projective duality

Cited by in corpus (7)

• The generalized Franchetta conjecture for some hyper-Kähler varieties, II
• Moduli spaces on the Kuznetsov component of Fano threefolds of index 2
• Some remarks on Fano threefolds of index two and stability conditions
• Serre-invariant stability conditions and Ulrich bundles on cubic threefolds
• Bridgeland Moduli spaces for Gushel-Mukai threefolds and Kuznetsov's Fano threefold conjecture
• Descent conditions for generation in derived categories
• Serre functors and dimensions of residual categories