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Subvarieties in non-compact hyperkaehler manifolds

Misha Verbitsky
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Abstract

Let M be a hyperkaehler manifold, not necessarily compact, and $S\cong CP^1$ 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 $I \in CP^1$. We show that for all $I \in S$ outside of a countable set, all compact complex subvarieties $Z \subset (M,I)$ are trianalytic. For M compact, this result was proven in alg-geom/9403006 using Hodge theory.

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Misha Verbitsky. 2004-01-01. Subvarieties in non-compact hyperkaehler manifolds. https://arxiv.org/abs/math/0312520

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