Abstract Patrick Graf

Patrick Graf will speak on

Algebraic approximation of Kahler threefolds of Kodaira dimension zero

Abstract: The classical Kodaira problem asks whether every compact Kahler manifold admits an algebraic approximation, i.e. a flat deformation containing projective fibres arbitrarily close to the central fibre. As shown by Voisin, this is false in general, although it may still be true for minimal Kahler spaces.

I will explain the proof of a recent result in this direction, namely that a compact Kahler threefold with canonical singularities and vanishing first Chern class admits an algebraic approximation. As a corollary, the fundamental group of any Kahler threefold is a quotient of an extension of fundamental groups of projective manifolds, up to subgroups of finite index.