Subvarieties of hypercomplex manifolds with holonomy in SL(n,H)
Algebraic Geometry
2012-07-26 v1 Complex Variables
Differential Geometry
Abstract
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, L^2=-1, L is also a complex structure operator on M, called an induced complex structure. We are studying compact complex subvarieties of (M,L), when L is a generic induced complex structure. Under additional assumptions (Obata holonomy contained in SL(n,H), 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).
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Cite
@article{arxiv.1202.0222,
title = {Subvarieties of hypercomplex manifolds with holonomy in SL(n,H)},
author = {Andrey Soldatenkov and Misha Verbitsky},
journal= {arXiv preprint arXiv:1202.0222},
year = {2012}
}
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16 pages