Mathematical Research Letters

Volume 11, Issue 4, July 2004 pp. 413-418.

Subvarieties in non-compact hyperkähler manifolds

Authors: Misha Verbitsky
Author institution: University of Glasgow

Summary: Let $M$ be a hyperkähler manifold, not necessarily compact, and $S\cong \C P^1$ 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 $I \in \C P^1$. 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 \cite{_Verbitsky:Symplectic_II_} using Hodge theory.

Contents Full-Text PDF