Symplectic and Kähler structures on $\mathbb{C}{P}^1$-bundles over $\mathbb{C}{P}^2$

Nicholas Lindsay, Dmitri Panov

We show that there exist symplectic structures on a $\mathbb{C}{P}^1$-bundle over $\mathbb{C}{P}^2$ that do not admit a compatible Kähler structure. These symplectic structures were orig…