Some Kähler structures on products of 2-spheres

Abstract

We consider a family of Kähler structures on products of 2-spheres, arising from complex Bott manifolds. ese are obtained via iterated ${\mathbb{P}}^1$-bundle constructions, generalizing the classical Hirzebruch surfaces. To each such Kähler structure, we associate a Bott diagram, which is a rooted forest with an edge labelling by positive integers. We show that the Bott diagrams classify these Kähler structures up to biholomorphism.