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

A hypercoinplex 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, L-2 = -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). (C) 2012 Elsevier B.V. All rights reserved.