Subvarieties of hypercomplex manifolds with holonomy in SL(n,H)

A hypercomplex manifold M is a manifold with a triple I,J,K of complex structure operators satisfying quaternionic relations. For each quaternion L=aI+bJ+cK, L2=−1, L is also a complex structure operator on M, called an induced complex structure. We study compact complex subvarieties of (M,L), for L a generic induced complex structure. Under additional assumptions (Obata holonomy contained in SL(n,H), the existence of an HKT-metric), we prove that (M,L) contains no divisors, and all complex subvarieties of codimension 2 are trianalytic (that is, also hypercomplex).