Subvarieties in non-compact hyperkähler manifolds

Abstract

Let M be a hyperkähler manifold, not necessarily compact, and S ∼= CP 1 the set of complex structures induced by the quaternionic action. Trianalytic subvariety of M is a subvariety which is complex analytic with respect to all I ∈ CP . We show that for all I ∈ S outside of a countable set, all compact complex subvarieties Z ⊂ (M, I) are trianalytic. For M… (More)

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