Abstract In this paper, we provide new examples of 1‐obstructed and atomic sheaves on an infinite series of locally complete families of projective hyper‐Kähler manifolds. More precisely, we prove that the fixed loci of the natural antisymplectic involutions on the moduli spaces of stable objects in the Kuznetsov component of a Gushel–Mukai fourfold are 1‐obstructed Lagrangian submanifolds, we construct a family of immersed atomic Lagrangian submanifolds on each moduli space of stable objects in , and we construct nonrigid projectively hyperholomorphic twisted bundles on any hyper‐Kähler manifold of ‐type for infinitely many . Additionally, we discuss examples of atomic Lagrangian submanifolds satisfying in a family of hyper‐Kähler manifolds of ‐type, as well as atomic sheaves supported on nonatomic Lagrangians.
Guo et al. (Thu,) studied this question.
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