EINSTEIN-KÄHLER TORIC FANO FOURFOLDS

Dedicated to Professor Hideki Ozeki on his sixtieth birthday

Abstract

We investigate the relationship between Matsushima's obstruction and the Futaki invariant for the existence of Einstein-Kähler metrics on toric Fano fourfolds. In particular, we determine all toric Fano fourfolds with vanishing Futaki invariant. Moreover, we construct a non-trivial example of an Einstein-Kähler toric Fano fourfold.