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arXiv · 1202.0222

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

Andrey Soldatenkov·Misha Verbitsky
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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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BibTeXRIS

Andrey Soldatenkov, Misha Verbitsky. 2012-02-01. Subvarieties of hypercomplex manifolds with holonomy in SL(n,H). https://doi.org/10.1016/j.geomphys.2012.07.002

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