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TAU: 24.5.2004 Mikhail Verbitsky, University of Glasgow and Institute of Theoretical and Experimental Physics Moscow

Title: Hyperkaehler Geometry

Abstract
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Compact hyperkaehler manifolds are equally relevant in algebraic geometry and differential geometry. From algebraic-geometric point of view, a hyperkaehler manifold is a compact Kaehler manifold equipped with a holomorphic symplectic structure. From differential-geometric point of view, a hyperkaehler
manifold is a Riemannian manifold equipped with a triple of Kaehler structures $I, J, K$ which satisfy the quaternionic relation $IJ = - JI = K$. The interplay between quaternionic and holomorphic symplectic geometry makes it possible to define and study the geometric objects intrinsic to hyperkaehler geometry (vector bundles, subvarieties, Hodge structures). In this aspect, hyperkaehler geometry becomes just as rich and interesting as the complex algebraic geometry.