Hsueh-Yung Lin: On algebraic approximations of compact Kähler threefolds
Time: Wed 2017-05-24 13.15 - 15.00
Location: Room 3418, KTH
Participating: Hsueh-Yung Lin, Universität Bonn
In complex geometry, compact Kähler manifolds are natural generalizations of projective varieties from the point of view of the Hodge theory and the deformation theory. Given a compact Kähler manifold X, the so-called Kodaira problem asks whether X has an (arbitrarily small) deformation to a projective variety. For surfaces such a deformation always exists (Kodaira, Buchdahl), but in each dimension greater than 4 there are compact Kähler manifolds which do not even have the homotopy type of a projective variety (Voisin). For threefolds the Kodaira problem remains open and will be the main focus of the talk. We will first present a way to understand the geometry of compact Kähler threefolds through the minimal model program and then discuss recent progress on the existence of algebraic approximations of these varieties.