Einstein-Kahler metric on manifolds with positive first Chern class

To prove the existence of an Einstein-Kahler metric on compact Kahler manifolds with positive first Chern class, we study the invariant alpha(Gp), introduced by Tan, first on P-m (C) then on the hypersurface of Fermat X(m,p). We prove the conjecture of Tan and Yau: alpha(Gp) (P-m (C)) greater than or equal to inf{1, p/(m + 1)}. This yields the theorem: if p greater than or equal to (m + 2)/2, there is on X(m,p) an Einstein-Kahler metric.