| A conjecture of Yau, Tian and Donaldson states that the existence of a canonical Kähler metric on an ample line bundle over a projective variety should be equivalent to K-stability, an algebro-geometric notion which is closely related to Geometry Invariant Theory. K-stability has also recently been used to construct compact moduli spaces of Fano varieties. However, K-stability is understood in very few specific cases. We show that certain finite covers of K-stable Fano varieties are also K-stable, giving algebro-geometric proofs of K-stability in several new examples. |