2003/12/31 by Misha Verbitsky
Mathematics · #math.AG #math.DG
published as Math. Res. Lett. vol. 11 (2004), no. 4, pp. 413-418 · 7 pages, a trivial error found and corrected
arxiv created 2004/01/01 · arxiv updated 2009/12/01
Let M be a hyperkaehler manifold, not necessarily compact, and S≅ CP1 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 ∈ CP1. We show that for all I ∈ S outside of a countable set, all compact complex subvarieties Z ⊂ (M,I) are trianalytic. For M compact, this result was proven in alg-geom/9403006 using Hodge theory.