Subvarieties in non-compact hyperkähler manifolds

Verbitski, M. (2004) Subvarieties in non-compact hyperkähler manifolds. Mathematical Research Letters, 11, pp. 413-418.

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Let M be a hyperkähler manifold, not necessarily compact, and S =∼C P1 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 ∈ C P1. 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 [V1] using Hodge theory.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Verbitski, Dr Mikhail
Authors: Verbitski, M.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Mathematical Research Letters

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
316541Hyperkaehler manifoldsMikhail VerbitskiEngineering & Physical Sciences Research Council (EPSRC)GR/R77773/01Mathematics