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. These are obtained via iterated ${\mathbb{P}}^1$-bundle constructions, generalizing the classical Hirzebruch surfaces. We show that the resulting Kähler structures all have identical Chern classes. We construct Bott diagrams, which are rooted forests with an edge labelling by positive integers, and show that these classify these Kähler structures up to biholomorphism.

12 pages