I'm reading the book of Guedj and Zeriahi, and I'm stuck on the following
Exercise 15.12. Let X be a Fano manifold (i.e. the first Chern class of $X$ contain a Kähler form) with no holomorphic vector field. Show that the set of Kähler–Einstein metrics (i.e. the Kähler forms $\omega$ which check $Ric(\omega) = \lambda \omega$) is discrete.
I don't have any idea about how to solve this. Do you have ideas or references?
